Deitmar, A., Universität Tübingen, Germany
 

Written for: Undergraduate math students, graduate math students 
Book category: Undergraduate Textbook
Publication language: English
 

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A First Course in Harmonic Analysis

(second edition) 

Springer New York 2005

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..."
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 Móricz for Acta Scientiarum Mathematicarum

This book is a primer in harmonic analysis using an elementary approach. Its first aim is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Secondly, it makes the reader aware of the fact that both, 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. There are two new chapters in this new edition. One on distributions will complete the set of real variable methods introduced in the first part. The other on the Heisenberg Group provides an example of a group that is neither compact nor abelian, yet is simple enough to easily deduce the Plancherel Theorem. Professor Deitmar is Professor of Mathematics at the University of Tübingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years.
 

Keywords: Harmonic analysis, Fourier analysis, Riemann integral
 

Contents: Fourier Series.- Hilbert Spaces.- The Fourier Transform.- Distributions.- Finite Abelian Groups.- LCA-groups.- The Dual Group.- The Plancherel Theorem.- Matrix Groups.- The Representations of SU(2).- The Peter-Weyl Theorem.- The Heisenberg Group.- The Riemann zeta function.- Haar integration.