A Panorama of Harmonic Analysis

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Cambridge University Press, Sep 2, 1999 - Mathematics - 357 pages
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Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax is a consideration of ideas from the point of view of spaces of homogeneous type, which culminates in a discussion of wavelets. This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.
 

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Contents

Fourier Series Basics
31
The Fourier Transform
95
Multiple Fourier Series
121
Spherical Harmonics
171
Fractional Integrals Singular Integrals
199
Modern Theories of Integral Operators
235
Wavelets
273
A Retrospective
313
Table of Notation
327
Index
347
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About the author (1999)

Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including "Calculus Demystified," another popular title in this series. He lives in St. Louis, Missouri.

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