A First Course in Harmonic Analysis

This book is a primer in harmonic analysis on the undergraduate level. It gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. In contrast to other books on the topic, A First Course in Harmonic Analysis is entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Nevertheless, almost all proofs are given in full and all central concepts are presented clearly.The first aim of this book is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. The second aim is to 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. The third goal of this book is to introduce 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 0387953752   Volumes 1 ISBN13 9780387953755 (What's this?)   Weight (grammes) 404 Publisher Springer-Verlag New York Inc.   Published in New York, NY Imprint Springer-Verlag New York Inc.   Series editor Axler, S., Gehring, F.W., Ribet, K.A. Format Hardback   Series title Universitext Publication date 01 Mar 2002   Height (mm) 230 Library of Congress 2001054914   Width (mm) 162 DEWEY 515.2433   Spine width (mm) 14 DEWEY edition DC21   Academic level Undergraduate, Postgraduate, Professional / Scholarly Pages 162

I		Fourier Analysis		1
1		Fourier Series		3
2		Hilbert Spaces		21
3		The Fourier Transform		37
II		LCA Groups		55
4		Finite Abelian Groups		57
5		LCA Groups		65
6		The Dual Group		79
7		Plancherel Theorem		89
III		Noncommutative Groups		105
8		Matrix Groups		107
9		The Representations of SU(2)		119
10		The Peter-Weyl Theorem		127
A		The Riemann Zeta Function		135
B		Haar Integration		139
		Bibliography		147
		Index		150

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