A Panorama of Harmonic Analysis

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Cambridge University Press, Sep 2, 1999 - Mathematics - 357 pages
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A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject.

A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
 

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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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