A First Course in Harmonic Analysis

Affordable softcover second edition of bestselling title (over 1000 copies sold of previous edition) A primer in harmonic analysis on the undergraduate level Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Almost all proofs are given in full and all central concepts are presented clearly. Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

ISBN 0387228373   Pages 206 ISBN13 9780387228372 (What's this?)   Volumes 1 Publisher Springer-Verlag New York Inc.   Weight (grammes) 660 Imprint Springer-Verlag New York Inc.   Published in New York, NY Format Paperback   Series title Universitext Publication date 06 Apr 2005   Height (mm) 234 Library of Congress 2004056613   Width (mm) 156 DEWEY 515.2433   Spine width (mm) 11 DEWEY edition DC22   Academic level Undergraduate, Postgraduate, Professional / Scholarly

1		Fourier series		5
2		Hilbert spaces		25
3		The Fourier transform		41
4		Distributions		59
5		Finite Abelian groups		73
6		LCA groups		81
7		The dual group		101
8		Plancherel theorem		111
9		Matrix groups		129
10		The representations of SU(2)		141
11		The Peter-Weyl theorem		149
12		The Heisenberg group		157
A		The Riemann zeta function		175
B		Haar integration		179

From the reviews of the first edition: "This lovely book is intended as a primer in harmonic analysis at the undergraduate level. All the central concepts of harmonic analysis are introduced using Riemann integral and metric spaces only. The exercises at the end of each chapter are interesting and challenging; no solutions are given. !" Sanjiv Kumar Gupta for MathSciNet "! In this well-written textbook the central concepts of Harmonic Analysis are explained in an enjoyable way, while using very little technical background. Quite surprisingly this approach works. It is not an exaggeration that each undergraduate student interested in and each professor teaching Harmonic Analysis will benefit from the streamlined and direct approach of this book." Ferenc Moricz for Acta Scientiarum Mathematicarum From the reviews of the second edition: "This is the second edition of a beautiful introduction to harmonic analysis accessible to undergraduates. ! The first part deals with classical Fourier analysis, the second provides the extension to locally compact abelian groups, and the third part is concerned with noncommutative groups." (G. Teschl, Internationale Mathematische Nachrichten, Issue 202, 2006)

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