Universitext

A First Course in Harmonic Analysis

Authors: Deitmar, Anton

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  • direct and streamlined approach to central concepts

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About this Textbook

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.
The reader interested in the central concepts and results of harmonic analysis will benefit from the streamlined and direct approach of this book.
Professor Deitmar holds a Chair in Pure Mathematics at the University of Exeter, U.K. He is a former Heisenberg fellow and was awarded the main prize of the Japanese Association of Mathematical Sciences in 1998. In his leisure time he enjoys hiking in the mountains and practising Aikido.

Reviews

From the reviews of the first edition:

A. Deitmar

A First Course in Harmonic Analysis

"An excellent introduction to the basic concepts of this beautiful theory, without too much technical overload . . . 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 benefits from the streamlined and direct approach of this book."—ACTA SCIENTIARUM MATHEMATICARUM

"This is a well thought thorough introduction to harmonic analysis … efficient, swift, elegant and concentrated. … It makes for an excellent text book, an instructor’s delight and a pleasure for students because of the precise formulation and the concise proofs in a little over one hundred pages. … A gem of a first course in harmonic analysis, heartily recommended." (A. Dijksma, Nieuw Archief voor Wiskunde, Vol. 7 (3), 2006)


Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-1-4757-3834-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
A First Course in Harmonic Analysis
Authors
Series Title
Universitext
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-3834-6
DOI
10.1007/978-1-4757-3834-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XI, 152
Topics