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Introduction to Fourier Analysis on Euclidean Spaces

Posted on 2010-03-16




Name:Introduction to Fourier Analysis on Euclidean Spaces
ASIN/ISBN:069108078X
Language:English
File size:8.3 Mb
Publish Date: 1971
ISBN: 069108078X
Pages: 312 pages
File Size: 8,3 MB
Other Info: Princeton University Press; Djvu
   Introduction to Fourier Analysis on Euclidean Spaces

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Elias M. Stein, Guido Weiss, ""

The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Summary: A superb classic in harmonic analysis.

Rating: 5

This book deals with the extension of real and complex methods in harmonic analysis to the many-dimensional case. So, its pre-requisites are a strong background in real and complex analysis and some acquaintance with elementary harmonic analysis, that is, this book is intended for graduate students and working mathematicians. Maybe some advanced undergraduates could cover certain parts of the material.

This book is one component of the Stein trilogy on harmonic analysis (together with "Singular Integrals and Differentiability Properties of Functions" and "Harmonic Analysis", both also reviewed by myself), and as such it must be regarded as an authoritative reference on the subject since Elias Stein and Guido Weiss are two of the leading experts in the field, and the material they selected was taken from their teaching and research experience.

The contents of the book are: The Fourier Transform; Boundary Values of Harmonic Functions; The Theory of H^p Spaces on Tubes; Symmetry Properties of the Fourier Transform; Interpolation of Operators; Singular Integrals and Systems of Conjugate Harmonic Functions; Multiple Fourier Series.

Includes motivation and full explanations for each topic, excercises for each chapter, called "further results", and extensive references. Outstanding printing quality and nice clothbound.

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