European Mathematical Society - 46 Functional analysis
https://euro-math-soc.eu/msc/46-functional-analysis
enLipschitz Algebras. Second Edition
https://euro-math-soc.eu/review/lipschitz-algebras-second-edition
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This second edition is much more than an update of the previous material that gives a profound insight about the main topics related to Lipschitz spaces and reflects the importance of spaces of Lipschitz functions.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Ángeles Prieto</div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/book-review/WeaverLipschitzAlgebras.pdf" type="application/pdf; length=116934" title="WeaverLipschitzAlgebras.pdf">Weaver. Lipschitz Algebras</a></span></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/nik-weaver" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Nik Weaver</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/world-scientific-publishing-co-pte-ltd" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">World Scientific Publishing Co. Pte. Ltd.</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2018</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9789814740630</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$126</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">462</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</a></li></ul></span><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46-02" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46-02</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/26a16" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">26A16</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/48bxx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">48Bxx</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/81q99" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81Q99</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/46exx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46Exx</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/46hxx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46Hxx</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/46j10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46J10</a></li></ul></span>Fri, 19 Jul 2019 14:22:53 +0000Ángeles Prieto49570 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/lipschitz-algebras-second-edition#commentsIndefinite Inner Product Spaces, Schur Analysis, and Differential Equations
https://euro-math-soc.eu/review/indefinite-inner-product-spaces-schur-analysis-and-differential-equations
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is volume 263 of the Birkhäuser series on <em>Operator Theory Advances and Applications</em>. It is devoted to Heinz Langer on the occasion of his eightieth birthday. Two other volumes in this series were celebrating Langer: <em>Contributions to operator theory in spaces with an indefinite metric</em> (OT106, 1995) on the occasion of his sixtieth birthday and <em>Operator theory and indefinite inner product spaces</em> (OT163, 2004) on the occasion of his retirement at the University of Vienna.</p>
<p>
The titles of these three volumes already illustrate that operator theory in indefinite inner product spaces form the focus of Langer's research. Langer was born in Dresden in 1935. After his his PhD and his habilitation at the TH Dresden he became a professor leading the institute of probability and mathematical statistics. His stay in Odessa in 1968-69 where he met M.G. Krein strongly influenced his career and his research interests. He also spent research stays at several Western universities as well, which was not obvious in the time of the DDR. In 1969 he left East Germany permanently to become a professor in Dortmund, later in Regensburg, and finally, in 1991, he accepted a position in Vienna where he stayed until his retirement.</p>
<p>
This is just a very brief summary, but Bernd Kirstein has a much longer, and richly illustrated contribution in this book. It is the ceremonial address on the occasion of the honorary doctorate awarded to Heinz Langer by the TU Dresden in 2016. He received many other prizes among which another Dr. h.c. from Stockholm University in 2015. Kirstein sketches in detail the people that were influential on Langer's career. Many of them became colleagues and friends. Among them are the most important names in the domain: Krein, Nudelman, Iokvidov, Potapov, Sakhnovich, Gohberg (who founded the OT series in 1979), Adamyan, Arov, Potapov, and many more. Kirstein describes this from his own perspective, hence the paper describes also the history of the Schur analysis group in Leipzig that he is leading together with his mathematical twin brother Bernd Fritzsche. Kirstein also illustrates the difficulties in maintaining relationships among mathematicians in an East block country and their colleagues who had left for Israel or another Western country before the fall of the Iron Curtain in 1989.</p>
<p>
A list of the publications of Heinz Langer (op to January 2017) is also included in the biographical part I of this book. A similar list in OT163 in 2006 had 171 entries, while the current one has 203 (the last one from 2017) which illustrates that Heinz Langer at his age is still an active researcher and collaborator. And the latter is what the main content of this book really is: an illustration of the influence that Langer had on other people who worked on topics related to the subjects that are close to the heart of his own research, always prepared to listen and collaborate. These topics include nonlinear eigenvalue problems, indefinite inner product spaces such as Krein and Pontryagin spaces and applications in mathematical physics.</p>
<p>
A collection of sixteen research papers, (some are longer surveys, others are short communications, all together over 420 pages) form the main part II of this volume. The titles of the papers and their authors are available on the publisher's website (see this book's meta-data elsewhere on this page) so that I do not need to repeat them here. The papers are listed in alphabetical order of the first author, but in their introduction, the editors subdivide them into five (overlapping) classes. The largest group falls under the broad title <em>Schur analysis, linear systems and related topics</em>. These papers are about Carthéodory and Weyl functions, Nevanlinna-Pick interpolation, scattering theory, L-systems and an inverse monodromy problem. In the group about <em>Differential operators, inverse problems and related topics</em> which is broad as well, we find papers related to the pantograph delay equation, and spectral and other properties for a selection of other operators. Two papers are explicitly dealing with <em>Pontryagin spaces</em> and one paper is about probability and is classified as <em>Non-commutative analysis</em>. <em>Positivity</em> is a keyword that can be assigned to almost all the papers in the volume, but it groups the remaining three texts where positivity has a key role.</p>
<p>
This volume will of course be of interest to anyone who knows or collaborated with Heinz Langer, but more generally for anyone working in one of the topics that he was, and still is, interested in, and this is a broad field as illustrated by the papers in this volume. So it may be that not all the papers are interesting for a particular reader, but in that case there is of course also the possibility to download an electronic version of a particular paper from the publisher's website, like one would do for a journal paper.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a set of papers collected to celebrate the eightieth birthday of Heinz Langer. The broad research field of Langer can be described by keywords as enumerated in the title of this book. Besides the set of selected papers that fall under these topics, there are also some biographical data like a list of publications of H. Langer and a long and richly illustrated paper by B. Kirstein sketching the career of Langer and his influence on the Schur analysis group in Leipzig.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/daniel-alpay" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">daniel alpay</a></li><li class="vocabulary-links field-item odd"><a href="/author/bernd-kirstein" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Bernd Kirstein</a></li><li class="vocabulary-links field-item even"><a href="/author/eds-1" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">(eds.)</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-nature-birkh%C3%A4user" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Springer Nature/ Birkhäuser</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2018</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-3-319-68848-0 (hbk), 978-3-319-68849-7 (ebk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">116.59 € (hbk); 91.62 € (ebk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">522</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</a></li><li class="vocabulary-links field-item odd"><a href="/imu/history-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">History of Mathematics</a></li><li class="vocabulary-links field-item even"><a href="/imu/partial-differential-equations" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Partial Differential Equations</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.springer.com/gp/book/9783319688480" title="Link to web page">http://www.springer.com/gp/book/9783319688480</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46n99" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46N99</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/47a57" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47A57</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/47a40" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47A40</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/93c05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">93C05</a></li></ul></span>Tue, 13 Mar 2018 08:03:28 +0000Adhemar Bultheel48324 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/indefinite-inner-product-spaces-schur-analysis-and-differential-equations#commentsA Friendly Approach To Functional Analysis
https://euro-math-soc.eu/review/friendly-approach-functional-analysis
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Many books were written on this topic already. The current text can be called friendly because when the author gives a definition, he usually connects it to what the reader is supposed to know. These prerequisites are basically not much more than finite dimensional vector spaces. Since this is what functional analysis is about: calculus lifted to the level of infinite dimensional vector spaces. A lot of effort goes into pointing out the similarities and the differences. Since also Lebesgue integrals are used, an appendix introduces this concept in the one dimensional case.</p>
<p>But friendly does not mean that the reader is spared from effort. The text is peppered with many (197) exercises. The formulation of the exercises and the solutions provided at the end form an essential part of the book and they actually fill the larger part of its pages. Thus the reader who is new to the topic is supposed to work hard to properly grasp all the ideas. By including the solutions, the book is suitable for self study, although the text grew out of lecture notes used by the author while teaching at the London School of Economics.</p>
<p>On the other hand, the subject is vast, and since this is only an introduction not all the most difficult proofs are provided in full extent and not all the most complicated issues are discussed in all detail. It is important to mentioned that, even though the subject is abstract, attention is also paid to the application aspect. In fact the introduction starts with an optimal control problem as a motivation to embark on functional analysis. In a later chapter when differentiation and its application to optimality conditions is discussed, the Euler-Lagrange equation is derived and it is applied to classical Hamiltonian and Poissonian mechanics. This forms also the basis for a discussion of quantum mechanics in the chapter on Hilbert spaces. Compact operators are a reason to go into the subject of finite dimensional Galerkin approximations of the operators, which is important for numerical computations. Weak solutions of differential equations are obtained using distributions, discussed in the last chapter. This means that also physics and engineering students will appreciate this approach.</p>
<p>The text is rather dense and to the point and covers an enormous variety of topics, even though the main text has only six chapters packed on 258 pages. Here is a superficial sketch of the contents. The first chapter makes the step from vector spaces to normed spaces and to Banach spaces. The next obvious things to tackle in any calculus course are continuity and differentiation, which are also here the subjects of chapters 2 and 3. These include some operator theory with the open mapping theorem, some spectral theory and even a proof of the Hahn-Banach theorem. The application of the Fréchet derivative in optimization and the application in mechanics was mentioned above. The chapter on inner product and Hilbert spaces may be the easiest ones to deal with since these spaces behave mostly like finite dimensional vector spaces when separable, and they are frequently used in all kinds of applications: approximation, Gram-Schmidt orthogonalization, generalized Fourier series, problems involving self-adjoint operators, etc. The next chapter shows that to study operators, things become easier when we restrict ourselves to compact operators. The final chapter on distributions (to stress that it is only an introduction to the subject, its title is A glimpse of distribution theory) has as one of its applications the weak solutions of differential equations but also allows to extend Fourier analysis. A few of the topics that are considered to be more advanced (like the open mapping theorem, the dual space and the Hahn-Banach theorem, and the spectral theory of compact self-adjoint operators) are marked by a star, so that they can be skipped it needed.</p>
<p>This is a nice and modern introduction to the topic. The impatient or more advanced reader can just read the text, skipping the exercises (perhaps skip only their solutions, not all their statements since they often are formulations of additional properties to be used in further proofs), and so get a quick idea. Where possible, examples clarify some basics and some subtleties of the definition or the property. If, on the other hand, the reader is a student who wants to become proficient in the subject, then solving the exercises, or an many as possible, is an excellent way to acquire the necessary skills. The flexible possibilities provided —the text can be used as lecture notes for a course, or as a tool for self study, and even as a handbook to look up some definitions or theorems— is another of its great advantages.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This is a modern introduction to functional analysis for mathematics or engineering students who are familiar with finite dimensional vector spaces. There are many exercises that form an integral part of the text. Topics discussed are Banach spaces, continuity and differentiation, Hilbert spaces, compact operators, and distributions. Applications include classical and quantum mechanics and optimization problems. The book can be used for self-study, as a guide for a course, and even as a reference work.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/amol-sasane" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Amol Sasane</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/world-scientific" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">world scientific</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1-78634-333-8 (hbk), 978-1-78634-334-5 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 98.00 (hbk), GBP 56.00 (pbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">396</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.worldscientific.com/worldscibooks/10.1142/Q0096" title="Link to web page">http://www.worldscientific.com/worldscibooks/10.1142/Q0096</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46-01</a></li></ul></span>Tue, 20 Feb 2018 14:08:08 +0000Adhemar Bultheel48277 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/friendly-approach-functional-analysis#commentsElements of Hilbert Spaces and Operator Theory
https://euro-math-soc.eu/review/elements-hilbert-spaces-and-operator-theory
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Books on functional analysis and operator theory appear regularly, but they are often dealing with a special topic such as differential operators, integral equations, spectral theory, or particular classes of operators. Not so remarkable since the topic is relatively new and mainly developed during the previous century by some of the best: Hilbert, Banach, Riesz, von Neumann, etc. The subject has grown very rapidly. Many of the general introductions therefore date back to the twentieth century as well. Only few are published after 2000. Given that the subject is still growing and has become a standard tool in theory and applications from analytic number theory to dynamical systems, a new modern introduction such as this one is very welcome.</p>
<p>
In its most elementary form engineers only need finite dimensional vector spaces, and if we restrict to linear operators, there is linear algebra to solve all the problems. However these problems are in many cases approximations for a phenomenon taking place in an infinite dimensional space, and when infinity is involved the mathematics become tricky and one needs good foundations to develop the proper theorems. Of course the subject is immense as is illustrated by the classic 3 volume set <em>Linear Operators</em> (1958-1971) by N. Dunford and J. Schwartz that contains over 2500 pages. So, it is a difficult balance to be kept between an encyclopedic work and an introduction that is both complete in the theoretical foundations and yet has attention for the applicability. This requires a lot of craftsmanship that is achieved remarkably well in this book.</p>
<p>
The author has made a selection in the massive amount of material available to provide a very readable introduction to the subject. To study the operators, one first needs to understand the spaces on which they operate. These are in practice mostly Hilbert spaces and Banach spaces. Then the linear operators can be defined and their spectral analysis can be studied. This defines the structure of the book shaped by the 5 chapters: a short general introduction recalling the necessary preliminaries, then inner product spaces, the linear operators, their spectral theory, and finally the Banach spaces. There is an extra chapter with hints and solutions to the many exercises that are amply sprinkled throughout the text.</p>
<p>
The emphasis is definitely on linear operators on Hilbert spaces and the spectral analysis of special classes of operators. So a first target is to introduce inner product spaces, that is the spaces of $L^2$ type, so that one can talk about orthogonality of a basis, define projections and discuss approximations. The most important operators are the normal, unitary, and isometric operators. The special classes for which the spectral analysis is studied in more detail include compact operators, trace class, self adjoint, and Hilbert-Schmidt operators. In the Banach space chapter, topics include the Hahn-Banach theorem, the Baire category theorem, and the open mapping and closed graph theorems. There is also a section on unbounded operators and at some point also invariant subspaces are discussed.</p>
<p>
The style is the typical mathematical approach of definition-theorem-proof kind of sequencing. However this is made lightly digestible by including many examples, remarks, and illustrations of what these formal definitions or theorems mean in practice and what the applications can be. Thus, although this is a quite mathematical subject, I think also engineers of a more theoretical kind will certainly appreciate this book very much. Among the applications we can mention Fourier analysis, orthogonal polynomials, approximation and convergence, Müntz theorem, Browder fixed point theorem, the mean ergodic theorem, numerical range, and much more. All the proofs are fully worked out. Only few theorems are mentioned without a proof if it is really too long and complicated and thus beyond the scope of these notes. Of course such a book cannot be read without an appropriate preparation which should include analysis and linear algebra. Most sections are followed by a set of exercises. These include often applications and examples, or ask to prove some extra properties. The level of difficulty nicely matches the level of the text. To assimilate the material, one should solve at least some of these exercises. As mentioned above, some 100 pages with hints and solutions are summarized in the last chapter.</p>
<p>
To conclude, I think this is a marvelous introduction to the topic. Certainly applied mathematicians and engineers who need a stronger mathematical background, or for mathematicians with an interest in applications, will appreciate this most. Obviously it can be used, or at least parts of it, as a perfect set of lecture notes for a course on the subject. Note however, that it is a general introduction. Let me give two examples of what it is <em>not</em>. It does <em>not</em> discuss in any detail the solution of differential or integral equations (Sobolev spaces are too specialized and out of the picture). Neither is there a direct link to the extensive literature on systems theory. The books of the Birkhäuser series on <em>Operator Theory Advances and Applications</em> for example are much more specialized. However this book introduces the preliminaries to engage in all these topics, just because it is paying special attention to the operators that are most common in applications such as these.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is an excellent introduction to linear operators on Hilbert and Banach spaces. Definitions and properties are introduced. In particular the spectral theory for particular classes of operators is discussed. Special attention is given to the applicability with many examples and illustrating the theory with several applications. Many exercises are provided with an extensive chapter giving hints and solutions at the end of the book. The book is perfectly fit to be used as a basis for a course on the topic.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/harkrishan-lal-vasudeva" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Harkrishan Lal Vasudeva</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer-nature" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Springer Nature</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-981-10-3019-2 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">116,59 € (hbk)</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">535</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.springer.com/gp/book/9789811030192" title="Link to web page">http://www.springer.com/gp/book/9789811030192</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46-02" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46-02</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46-cxx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46-Cxx</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/47axx" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47Axx</a></li></ul></span>Thu, 20 Apr 2017 12:58:13 +0000Adhemar Bultheel47633 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/elements-hilbert-spaces-and-operator-theory#commentsHilbert Space and Quantum Mechanics
https://euro-math-soc.eu/review/hilbert-space-and-quantum-mechanics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
Quantum mechanics has several fathers: Planck, Bohr, Heisenberg, Einstein, Schrödinger, Dirac, Hilbert, von Neumann, and many others. As a consequence, there are different approaches to the theory. Dirac's approach is rather popular among physicists because it requires relatively little mathematics. In this book, the author follows the ideas of von Neumann and Hilbert who thought that quantum mechanics needed an abstract framework which we now call a Hilbert space. It turned out that spectral theory of self adjoint operators in Hilbert space were substantial in the development of quantum mechanics.</p>
<p>
So this book brings a self-contained axiomatic mathematical foundation in which quantum mechanics can be studied. All the mathematics needed to develop a spectral theory of self adjoint operators in Hilbert space are built up from scratch. Eventually, in the last two chapters, observables can be introduced as self-adjoint operators and physical compatibility nicely matches commutativity of the operators etc. However, these two chapters, are only an introduction of the basic elements and structures with which quantum mechanics can take off. It certainly is not a summary of the whole theory. Thus most of the book is functional analysis and everything needed for the last chapters. And that is a whole lot of mathematics indeed.</p>
<p>
The approach is axiomatic and very thorough. Starting with the basics of sets and relations and the notion of a group, the proper work starts with metric spaces, linear operators, measure theory and integration, Hilbert spaces (in particular L²), self-adjoint operators and orthogonal projections. Then the topics become somewhat less standard discussing integration with respect to these projection valued measures (giving resolution of the identity), spectral theorems, commuting operators, trace class operators, and finally statistical operators. All this to prepare for the last two chapters in which quantum mechanics in Hilbert spaces are introduced and the concepts of position and momentum in non-relativistic quantum mechanics.</p>
<p>
So, in the end, there is only 126 pages of quantum mechanics but 610 pages of mathematical introduction, not that there is much difference. The quantum mechanics are treated in the same strict axiomatic approach and all the previous notation and structures are used. To name just one example, the bra-ket notation dominating the standard books on quantum mechanics is not used. The quantum mechanics is still using the same structures and operators but it has its own terminology. Hence, there are fewer theorems and many more definitions in the penultimate chapter to introduce the terminology of the new subject.</p>
<p>
The stunning achievement of this book is however that, even though the book starts with rules of logic to construct a proof and an explanation what the usual mathematical symbols mean, all the theorems from the first till the last chapter are fully proved. This is fairly unusual for mathematics books where proofs often rely on results from different fields. Thus it is no wonder that the bibliography of this book is relatively short (barely 2 pages), given all the topics covered. Since one does not read such a book cover to cover in one day, it needs often backtracking to look up a definition, a theorem, or a proof. Then of course a detailed subject index is essential. The index here is not as extensive at it could have been, but fortunately it is not needed very often because whenever in the text a theorem, definition, or relation is used that was introduced a few pages earlier or in a previous chapter, then a precise pointer is given. The discussion however is abstract. That is <em>very</em> abstract. Trained mathematicians are perhaps used to this, but if this book is intended to enlighten and convince the 'otherwise-not-so-mathematically-oriented' physicists about the advantages of this approach, then that might be a bit of a problem. There are some examples to illustrate the abstract concepts in the text, but they are very rare. In my opinion, there could, and perhaps should have been more. That would have made the book even thicker (and heavier) than it is now, which might require two volumes. Another fact, illustrating the level of abstraction is that there are no figures either, except for one page with figures in the quantum mechanics chapter.</p>
<p>
But all in all, it is an excellent tool for self study. A mathematics student can just enjoy the mathematics, even if not interested in quantum mechanics. The last two chapters can easily be dropped. A trained mathematician interested in quantum mechanics will be familiar with most of the mathematics in the book, but will find the trailing chapters most informative. He or she will need however another <em>matching</em> book to embark on the full quantum mechanics. Not all books on quantum mechanics will hook up with the approach used here. The book too thick to be used as a handbook for one course, but some chapters could be selected for such a course. In fact some suggestions are made in the introduction for a course in real analysis, or in operator theory. There are no exercises though.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
This is a thorough self-contained mathematical introduction to functional analysis that contains all the mathematics needed to start studying quantum mechanics. Only in the last two chapters, all this is used to introduce some basic structures in which quantum mechanics can be developed.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/franco-gallone" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Franco Gallone</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/world-scientific-publishing" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">world scientific publishing</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-981-4635-83-7 (hbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 91.00</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">760</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/analysis-and-its-applications" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Analysis and its Applications</a></li><li class="vocabulary-links field-item odd"><a href="/imu/mathematical-physics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematical Physics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.worldscientific.com/worldscibooks/10.1142/9405" title="Link to web page">http://www.worldscientific.com/worldscibooks/10.1142/9405</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46-01</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/81-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81-01</a></li></ul></span>Mon, 18 May 2015 05:35:50 +0000Adhemar Bultheel46225 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/hilbert-space-and-quantum-mechanics#commentsStable Perturbations of Operators and related topics
https://euro-math-soc.eu/review/stable-perturbations-operators-and-related-topics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book concerns with the theory of stable perturbations of operators in<br />
Banach spaces . Thus the perturbation analysis for generalized inverses, the<br />
Moore-Penrose inverse and Drazin inverse of operators under stable pertur-<br />
bation. After a preliminary chapter including several basic results in Func-<br />
tional Analysis ( Hilbert spaces, operators and C + algebras ) the book studies<br />
carefully the relationships among the densely-defined operators with closed<br />
range and the reduced minimum modulus of densely defined operators . The<br />
Moore-Penrose inverse and its stable perturbations in Hilbert spaces and in<br />
C ∗ -algebras is also presented . Several results of the K-theory in C + algebras<br />
are also included. The last chapters of the book contain some miscellaneous<br />
applications and related topics to the perturbation theory, like the approxi-<br />
mate polar decomposition in C ∗ -algebras, and some applications of Moore-<br />
Penrose inverses in frame theory.The list of references in the Bibliography is<br />
quite extensive.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Francisco L. Hernandez </div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad complutense de Madrid</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The book studies different analysis perturbation of operators , including Moore-Penrose inverse, and Drazin inverse of operaors .Several miscellaneous applications are also included.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/yifeng-xue" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">yifeng xue</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/word-scientific" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">word scientific</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2012</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">13 978-981-4383-59-2</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span>Fri, 08 Nov 2013 17:13:28 +0000Anonymous45532 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/stable-perturbations-operators-and-related-topics#comments Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces
https://euro-math-soc.eu/review/fr%C3%A9chet-differentiability-lipschitz-functions-and-porous-sets-banach-spaces
<div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Daniel Azagra</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad complutense de Madrid </div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/ReviewLinPreissTi.pdf" type="application/pdf; length=124219" title="ReviewLinPreissTi.pdf"> Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces </a></span></div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book explains the main results known about differentiability of Lipschitz functions $f:X\to Y$, where $X,Y$ are Banach spaces, as well as it presents, with full proofs, new, important results of the authors which were only announced in previous publications.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/joram-lindenstrauss" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">joram lindenstrauss</a></li><li class="vocabulary-links field-item odd"><a href="/author/david-preiss" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">david preiss</a></li><li class="vocabulary-links field-item even"><a href="/author/jaroslav-tiser" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">jaroslav tiser</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2012</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">9780691153568</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46g05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46g05</a></li></ul></span>Wed, 05 Jun 2013 16:23:21 +0000Anonymous45513 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/fr%C3%A9chet-differentiability-lipschitz-functions-and-porous-sets-banach-spaces#commentsFunctional Analysis. Introduction to further topics in Analysis
https://euro-math-soc.eu/review/functional-analysis-introduction-further-topics-analysis
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is the fourth volume of a series in Mathematical Analysis by the same authors based on lectures at Princeton<br />
University. The book is written as self-contained and touches also several other branches of mathematical analysis.<br />
As the authors say, besides the basic theorems in Functional Analysis, the main objective is to present the strong link<br />
between Functional analysis and Harmonic analysis. It contains also nice deep introductions to other topics of analysis like<br />
several complex variables, probability theory and Brownian motion. Many classical and modern Function Spaces, very useful in Analysis, are presented in a very natural way with a clear motivation. A special chapter is dedicated to Distributions or generalized functions. Also a long chapter is dedicated to Oscillatory integrals in Fourier Analysis. There is a list of exercises and interesting problems after every chapter.</p>
<p>This is an excellent book with very clear expositions and historic motivations (as the previous three volumes by the same authors). The book is highly recommendable for all those interested in Modern Analysis.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Francisco L. Hernández</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The book is devoted to present the basic results in Functional Analysis and further advanced topics<br />
related with Harmonic Analysis and Probability theory. It is an excellent book with very clear expositions.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/elias-m-stein-rami-shakarchi" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">elias m. stein & rami shakarchi</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/princeton-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">princeton university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-691-11387-6</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/46-01" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46-01</a></li></ul></span>Tue, 18 Sep 2012 12:29:51 +0000Anonymous45462 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/functional-analysis-introduction-further-topics-analysis#commentsFunctional Equations in Mathematical Analysis
https://euro-math-soc.eu/review/functional-equations-mathematical-analysis
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This volume has been edited in commemoration of the 100th anniversary of the birth of the eminent mathematician and physicist Stanislaw Ulam (April 3, 1909 to May 13, 1984). The editors of the volume are Themistocles M. Rassias (National Technical University of Athens, Greece) and Janusz Brzdek (Pedagogical University of Krakow, Poland). </p>
<p>The volume consists of 47 articles written by experts who present research works in the field<br />
of Mathematical Analysis and related subjects, in particular, in Functional Equations and<br />
Inequalities. These works provide an insight in the study of various problems of nonlinear<br />
analysis. Several of the results have been influenced by the work of S. Ulam. In particular,<br />
a special emphasis is given to one of his questions concerning approximate homomorphisms.</p>
<p>The book is divided in two parts. Part I focuses on several aspects of the Ulam stability<br />
theory. The original stability problem was posed by S. M. Ulam in 1940 and concerned<br />
approximate homomorphisms. The pursuit of solutions to this problem, but also to its<br />
generalizations and modifications for various classes of (difference, functional, differential, and integral) equations and inequalities, is an expanding area of research and has led to the development of what is now known as the Hyers-Ulam stability theory. </p>
<p>Part II consists of papers on various subjects of Mathematical Analysis, mainly<br />
Functional Analysis, Inequalities, and Geometric Analysis.</p>
<p>All together, it is a very nice volume collecting a lot of material of high level, which can be of interest to researchers in different areas related to Ulam's work.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Vicente Muñoz</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">UCM, Spain</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This volume has been edited in commemoration of the 100th anniversary of the birth of the eminent mathematician and physicist Stanislaw Ulam (April 3, 1909 to May 13, 1984). The volume consists of 47 articles written by experts who present research works in the field of Mathematical Analysis and related subjects, in particular, in Functional Equations and Inequalities.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/themistocles-m-rassias" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">themistocles m. rassias</a></li><li class="vocabulary-links field-item odd"><a href="/author/janusz-brzdek" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">janusz brzdek</a></li><li class="vocabulary-links field-item even"><a href="/author/editors" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">editors.</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2012</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">987-1-4614-0054-7</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">$220</div></div></div><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://rd.springer.com/book/10.1007/978-1-4614-0055-4" title="Link to web page">http://rd.springer.com/book/10.1007/978-1-4614-0055-4</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span>Wed, 08 Feb 2012 21:19:39 +0000Anonymous45439 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/functional-equations-mathematical-analysis#commentsCONCRETE FUNCTIONAL CALCULUS
https://euro-math-soc.eu/review/concrete-functional-calculus
<div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Francisco L. Hernández</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">Universidad Complutense de Madrid</div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/reviewDudley.pdf" type="application/pdf; length=59325" title="reviewDudley.pdf">CONCRETE FUNCTIONAL CALCULUS </a></span></div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>This book is concerned with differentiability of nonlinear operators on Function Space. An extensive analysis of p-variation of functions is done with many applications to stochastic processes and nonlinear integral equations.<br />
It is divided into twelve chapters on different topics on Functional calculus and an appendix on non-atomic measure spaces. Its many historical comments and remarks clarify the development of the theory.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/rm-dudley" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">r.m. dudley</a></li><li class="vocabulary-links field-item odd"><a href="/author/r-norvaisa" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">r. norvaisa</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/springer" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">springer</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-1-4419-6949-1</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span>Fri, 13 Jan 2012 20:38:33 +0000Anonymous45434 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/concrete-functional-calculus#comments