Functional Analysis. Introduction to further topics in Analysis

Author(s): 
Elias M. Stein & Rami Shakarchi
Publisher: 
Princeton University Press
Year: 
2011
ISBN: 
978-0-691-11387-6
Short description: 

The book is devoted to present the basic results in Functional Analysis and further advanced topics
related with Harmonic Analysis and Probability theory. It is an excellent book with very clear expositions.

MSC main category: 
46 Functional analysis
MSC category: 
46-01
Other MSC categories: 
46-02 , 46F10
Review: 

This book is the fourth volume of a series in Mathematical Analysis by the same authors based on lectures at Princeton
University. The book is written as self-contained and touches also several other branches of mathematical analysis.
As the authors say, besides the basic theorems in Functional Analysis, the main objective is to present the strong link
between Functional analysis and Harmonic analysis. It contains also nice deep introductions to other topics of analysis like
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.

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.

Reviewer: 
Francisco L. Hernández
Affiliation: 
Universidad Complutense de Madrid

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