European Mathematical Society - 47A57
https://euro-math-soc.eu/msc-full/47a57
enIndefinite 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#commentsThe moment problem
https://euro-math-soc.eu/review/moment-problem
<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>
The moment problem, or one should say moment problems (plural) because there are several different classical moment problems. Some ideas can be found in work of Chebyshev and Markov, but Stieltjes at the end of the nineteenth century was one of the first to formally consider the moment problem named after him. Given a sequence of numbers ($m_k$), is there a positive measure $\mu$ such that $m_k=\int x^k \mu(dx), k=0,1,2,\ldots$? In the case of Stieltjes, the measure was supposed to have a support on the positive real line. First of all one wants to find out under what conditions such a measure exists, then when the solution is unique, and when it is not unique to characterize all possible solutions. Soon (around 1920) other versions were formulated by Hamburger (when the support of the measure is the whole real line) and Hausdorff (when the support is a finite interval) and some ten years later the trigonometric moment problem was tackled by Verblunsky, Akhiezer and Krein where the support is the complex unit circle. There is a basic difference between the trigonometric moment problem and the other classical moment problems on (parts of) the real line. In the latter situation, the existence of a solution is guaranteed by requiring the positivity of Hankel matrices whose entries are the moments. In the trigonometric case, the Hankel matrices are replaced by Toeplitz matrices. The latter involve also the moments $m_{-k}=\overline{m}_k, k=1,2,\ldots$ which are automatically matched as well. Not so for the other moment problems. When also imposing moments with a negative index in those cases, this is called a <em>strong</em> moment problem. When only a finite number of moments are prescribed, this is called a <em>truncated</em> moment problem.</p>
<p>
The importance of the moment problem is a consequence of the fact that it is at the crossroads of several branches and applications of mathematics. It relates to linear algebra, functional analysis and operator theory, stochastic processes, approximation theory, optimization, orthogonal polynomials, systems theory, scattering theory, signal processing, probability, and many more. No wonder that the greatest names in mathematics have contributed to the problem with papers and monographs. Because of the many connections to different fields also many approaches and many generalizations have been considered. The previously described moments are called power moments because of the $x^k$, but one could also prescribe moments based on a set of other functions $M_k(x)$. Traditionally, the Hausdorff moment problem is formulated for the interval [0,1], but one may consider any finite interval $[a,b]$ just like the Stieltjes moment problem could be formulated for any half line $[\alpha,\infty)$. Other generalizations lifts these problems to a block version, by assuming that the moments are matrices and the measure is matrix-valued, or the variable $x$ can have several components, resulting in a multivariate moment problem.</p>
<p>
The fact that today, 100 years after Hamburger and Hausdorff, this is still an active research field is another proof of the importance of moment problems. Many books did appear already that were devoted to moment problems or where moment problems played an essential role. Some classics are Shohat and Tamarkin <em>The Problem of Moments</em> (1943), Akhiezer <em>The classical moment problem and some related questions in analysis</em> (1965), Krein and Nudelman <em>The Markov moment problem and extremal problems</em> (1977). The present book is a modern update of the situation. It gives an operator theoretic approach to moment problems, leaving aside the applications. The univariate classical problems of Hamburger ($\mathbb{R}$), Stieltjes ($[0,\infty)$) and Hausdorff ($[a,b]$), appear both in their full and their truncated version. Also the trigonometric moment problem is represented but by only one chapter.<br />
The introduction to these problems is quite general. It is showing how integral representations for linear functionals can be obtained, and in particular how this works for finite dimensional spaces, and for truncated moment problems. Another essential tool is giving some examples of how moment problems can be defined on a commutative *-semigroup. Indeed, all what is needed is a structure with an involution (which could be the identity) and it should allow the definition of a positive definite linear functional so that it can give rise to an inner product on the space of polynomials (and its completion). With gross oversimplification one could say that a sequence is a moment sequence if the associated linear functional is positive and the solution corresponds to the measure that appears in an integral representation of the functional. For real problems, the involution is the identity: $x^*=x$, for complex problems, the involution $x^*=1/\overline{x}$ allows to treat the trigonometric moment problem at the same level as the real moment problems.<br />
This general approach is not really needed for the classical one dimensional moment problems that are treated in part I and the truncated version in part II, but the generality of the introduction allows more easy generalizations to the multivariate case and its truncated version that are discussed in parts III and IV respectively. What is treated in the first two parts are the classical results: the representation of positive polynomials, conditions for the existence of a solution of the moment problem, Hankel matrices, orthogonal polynomials and the Jacobi operator, determinacy (i.e. uniqueness) of the solution, the characterization of all solutions in the indeterminate case, and the relation with complex interpolation problems for Pick functions. For truncated moment problems one may look for some special, so called N-extremal, solutions which lie on the boundary of the solution set, or a canonical solution or solutions that maximize the mass in a particular point of an atomic solution.</p>
<p>
For the multivariate case, it takes some more work and we do not have the classical cases where the measure should be supported and generalizations can go in many different directions. Nevertheless, the corresponding chapters in parts III and IV go through the same steps as in the univariate case as much as possible. What are representing measures and when are polynomials positive? By defining the moment problem for a finitely generated abelian unital algebra, and using a fiber theorem that characterizes moment functionals, some generalizations of the one-dimensional case can be obtained (like for example a rational moment problem) or moment problems on some cubics. Determinacy of the multivariate moment problem is given in the form of a generalized Carleman condition, moments for the Gaussian measure on the unit sphere, and complex one- and two-sided moment problems are all discussed. Characterizing a canonical or extreme solution(s) is not as simple as in the one-dimensional case. Only for the truncated multivariate problems Hankel matrices are introduced and atomic solutions with maximization of a point mass can be characterized.</p>
<p>
The book appears in the series <em>Graduate Texts in Mathematics</em> which means that it is conceived as a as a text that could be used for lecturing with proofs fully included and extra exercises after every chapter as well as notes the refer to the history and the related literature. It is however marvellously capturing the present state of the art of the topic. So it will be also a reference work for researchers. It captures a survey of the univariate case and indicates research directions for the multivariate problem. The list of references at the end of the book has both historical as recent publications, but it is restricted to what has been discussed in the present book. Schmüdgen has published two books before on operator theory, so he knows how to write a book on a difficult subject and still keep it accessible for the audience that he is addressing (graduate students and researchers). Lists of symbols are really helpful to remember notation. The fact that on page 4 Chebyshev and Markov are situated in 1974 and 1984 respectively is just a glitch in an otherwise carefully edited text.</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 operator approach surveying classical one-dimensional moment problems, but the setting is general by formulating the problem on an abelian *-semigroups. This allows to also capture an introduction to multivariate moment problems which is much more recent and a subject that is still in evolution. The characterization of moment sequences, associated linear moment functionals, and determinate as well as indeterminate problems for the full or the truncated problems are discussed. Particular canonical and N-extremal solutions or solutions with a maximal mass point are discussed.</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/konrad-schm%C3%BCdgen" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Konrad Schmüdgen</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-internationa" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Springer Internationa</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">978-3-319-64545-2 (hbk); 978-3-319-64546-9 (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">84,79 € (hbk); 67,82 € (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">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/9783319645452" title="Link to web page">http://www.springer.com/gp/book/9783319645452</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/47-operator-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47 Operator theory</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/47a57" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47A57</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/42a70" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">42A70</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/30e05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">30e05</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/44a60" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">44A60</a></li></ul></span>Tue, 13 Mar 2018 07:38:36 +0000Adhemar Bultheel48323 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/moment-problem#commentsLarge Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
https://euro-math-soc.eu/review/large-truncated-toeplitz-matrices-toeplitz-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 is a volume 259 in the Bikhäuser OT Series <em>Operator Theory Advances and Applications</em>. It contains 30 contributions celebrating Albert Böttcher's 60th birthday.</p>
<p>
Albert Böttcher is a professor of mathematics at the TU Chemnitz in Germany. His main research topic is functional analysis. At his 18th he won the silver medal at the International Math Olympiad in Moscow. He studied mathematics at the TU Karl-Marx-Stadt (now TU Chemnitz) and finished a PhD in 1984 entitled <em>The finite section method for the Wiener-Hopf integral operator</em> under supervision of V.B. Dybin at Rostov-on-Don State University in Russia (this was all while the Berlin wall was still up). Since then he stayed at the TU Chemnitz. At the time of writing he has (co)authored 9 books and over 220 papers. The complete list is in the beginning of the book but one may also consult his <a href="https://www-user.tu-chemnitz.de/~aboettch/" target="_blank">website</a> where he keeps his list of publications up to date.</p>
<p>
The contributions start with reminiscences and best wishes by friends, colleagues and students of Albrecht Böttcher. Besides personal recollections, there is some discussion of his work, some photographs and reproductions of slides he used in presentations to illustrate that he is not only an excellent mathematician but also a passionate teacher and lecturer.</p>
<p>
That leaves about 700 pages of original research papers all of which relate from far or near to subjects that Böttcher has worked on. The Toeplitz operators and Toeplitz matrices of the title are indeed well represented, but there are all the other "Related Topics" which are close to his work too. About fifty renowned authors are involved.</p>
<p>
The Toeplitz operator (and hence also its spectrum) is characterized by a function, which is called its symbol. It features in a multiplication or convolution in the definition of the operator. With respect to a standard monomial basis, Toeplitz operators are represented by (infinite) Toeplitz matrices that have constant entries along diagonals. Of course the spectral and other properties of truncations of the infinite matrices to large finite ones relate to corresponding properties of Toeplitz operators, and similarly it can be related to other operators such as convolution and Wiener-Hopf operators. These matrices and operators have applications in differential and integral equations, systems and control, signal processing, and many more. Depending on the application the symbol may get an interpretation of transfer function of a system, power spectrum or autocorrelation of a signal, the kernel of an integral equation, or just a weight function in a Hilbert space. So, Toeplitz matrices and operators are also related to numerical methods for solving functional equations after discretization. Or to orthogonal polynomials (on the unit circle), which then in turn links to (trigonometric) moment problems, quadrature, and approximation theory (on the unit circle, but in a similar way also to analogs on the real line).</p>
<p>
Obviously this is not the place to discuss every paper in detail. The table of contents is available on the publisher's website and for convenience the research papers are also listed below. From the titles you will recognize the papers on determinants and eigenvalues for Toeplitz matrices, in particular their asymptotic behaviour as their size goes to infinity. Of course circulant and Hankel operators and combinations of these as operators or matrices are not far off the central theme and they are thus also treated in some of the chapters. The majority of the papers present new results. Note that most of them are (functional) analysis. Only a few exceptions are more linear algebra or make a link to physics or explicitly discuss numerical aspects (see [14, 16, 18, 23, 25, 27] below).</p>
<p>
Some of the papers are quite long (more than 30 pages and some even up to 50 pages). They are basically true research papers, sometimes a bit more expository, but they are not of the introductory broad survey type. So this is not the book you should read to be introduced to the subject, but is is more a sketch of the state-of-the-art for who is already famiiar. The style of course depends on the authors, but the book is homogeneous because of the subjects that all somehow relate to Böttcher's work. These topics discussed here are also close to the core idea of this book series <em>Operators Theory Advances and Applications</em>, founded by Israel Gohberg as a complement to the journal <em>Integral Equations and Operator Theory</em>. Only one of Böttcher's books appeared in this series though (<em>Convolution Operators and Factorization of Almost Periodic Matrix Functions </em> (2002) authored with Yu. I. Karlovich, and I. M. Spitkovsky appeared as volume 131) but several of his books are with Springer / Birkhäuser. That these topics are still a main focus of research is illustrated by the successful annual IWOTA conferences (<em>International Workshop on Operator Theory and its Applications</em>), the proceedings of which are also published in this OT series. The IWOTA 2017 is organized by A. Böttcher, D. Potts and P. Stollmann at the TU Chemnitz.</p>
<p>
Thus for anyone interested in the general topics of this book series, this collection will be a worthy addition. For those who are more selective, there is of course still the possibility to get some separate chapters, which is the advantage of having it also available as an ebook.</p>
<p>
Here are the titles and authors of the research papers in this volume:</p>
<p>
<br />
7. <em>Asymptotics of Eigenvalues for Pentadiagonal Symmetric Toeplitz Matrices, </em> Barrera, M. (et al.), Pages 51-77<br />
8. <em>Echelon Type Canonical Forms in Upper Triangular Matrix Algebras, </em> Bart, H. (et al.), Pages 79-124<br />
9. <em>Asymptotic Formulas for Determinants of a Special Class of Toeplitz + Hankel Matrices, </em> Basor, E. (et al.), Pages 125-154<br />
10. <em>Generalization of the Brauer Theorem to Matrix Polynomials and Matrix Laurent Series, </em> Bini, D.A. (et al.), Pages 155-178<br />
11. <em>Eigenvalues of Hermitian Toeplitz Matrices Generated by Simple-loop Symbols with Relaxed Smoothness, </em> Bogoya, J.M. (et al.), Pages 179-212<br />
12. <em>On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II, </em> Bothner, T. (et al.), Pages 213-234<br />
13. <em>Useful Bounds on the Extreme Eigenvalues and Vectors of Matrices for Harper's Operators, </em> Bump, D. (et al.), Pages 235-265<br />
14. <em>Fast Inversion of Centrosymmetric Toeplitz-plus-Hankel Bezoutians, </em> Ehrhardt, T. (et al.), Pages 267-300<br />
15. <em>On Matrix-valued Stieltjes Functions with an Emphasis on Particular Subclasses, </em> Fritzsche, B. (et al.), Pages 301-352<br />
16. <em>The Theory of Generalized Locally Toeplitz Sequences: a Review, an Extension, and a Few Representative Applications, </em> Garoni, C. (et al.), Pages 353-394<br />
17. <em>The Bézout Equation on the Right Half-plane in a Wiener Space Setting, </em> Groenewald, G.J. (et al.), Pages 395-411<br />
18. <em>On a Collocation-quadrature Method for the Singular Integral Equation of the Notched Half-plane Problem, </em> Junghanns, P. (et al.), Pages 413-462<br />
19. <em>The Haseman Boundary Value Problem with Slowly Oscillating Coefficients and Shifts, </em> Karlovich, Yu.I., Pages 463-500<br />
20. <em>On the Norm of Linear Combinations of Projections and Some Characterizations of Hilbert Spaces, </em> Krupnik, N. (et al.), Pages 501-510<br />
21. <em>Pseudodifferential Operators in Weighted Hölder-Zygmund Spaces of Variable Smoothness, </em> Kryakvin, V. (et al.), Pages 511-531<br />
22. <em>Commutator Estimates Comprising the Frobenius Norm - Looking Back and Forth, </em> Lu, Zhiqin (et al.), Pages 533-559<br />
23. <em>Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions on the Boundary, </em> Militzer, E. (et al.), Pages 561-591<br />
24. <em>Traces on Operator Ideals and Related Linear Forms on Sequence Ideals (Part IV), </em> Pietsch, A., Pages 593-619<br />
25. <em>Error Estimates for the ESPRIT Algorithm, </em> Potts, D. (et al.), Pages 621-648<br />
26. <em>The Universal Algebra Generated by a Power Partial Isometry, </em> Roch, S., Pages 649-662<br />
27. <em>Norms, Condition Numbers and Pseudospectra of Convolution Type Operators on Intervals, </em> Seidel, M., Pages 663-680<br />
28. <em>Paired Operators in Asymmetric Space Setting, </em> Speck, F.-O., Pages 681-702<br />
29. <em>Natural Boundary for a Sum Involving Toeplitz Determinants, </em> Tracy, C.A. (et al.), Pages 703-718<br />
30. <em>A Riemann-Hilbert Approach to Filter Design, </em> Wegert, E., Pages 719-740</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 collection of papers dedicated to Albrecht Böttcher's 60th birthday. The contributions are by friends, colleagues and students. After the impressive list of his publications, many of which dealing with asymptotics of Toeplitz and related operators, the book has some birthday addresses sketching Böttcher as a person and some of his work. The major part however consists of research papers written on invitation by specialists on topics related by far or near to the work of Böttcher. <br />
</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/dario-bini" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Dario A. Bini</a></li><li class="vocabulary-links field-item odd"><a href="/author/torsten-ehrhardt" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Torsten Ehrhardt</a></li><li class="vocabulary-links field-item even"><a href="/author/alexei-yu-karlovich" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Alexei Yu. Karlovich</a></li><li class="vocabulary-links field-item odd"><a href="/author/ilya-matvey-spitkovsky" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Ilya Matvey Spitkovsky</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/birkh%C3%A4user-basel" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">birkhäuser basel</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">978-3-319-49180-6 (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">174,89 € (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">766</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/9783319491806" title="Link to web page">http://www.springer.com/gp/book/9783319491806</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/47-operator-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47 Operator theory</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/47b35" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">47B35</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/30e05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">30e05</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/45e10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">45E10</a></li><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/15b05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">15B05</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/65d15" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">65D15</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/65g50" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">65G50</a></li><li class="vocabulary-links field-item even"><a href="/msc-full/65j10" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">65J10</a></li></ul></span>Sat, 20 May 2017 12:07:31 +0000Adhemar Bultheel47678 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/large-truncated-toeplitz-matrices-toeplitz-operators-and-related-topics#comments