September 18, 2012 - 15:29 — Anonymous

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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