© 2005

A First Course in Harmonic Analysis


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Fourier Analysis

    1. Pages 5-23
    2. Pages 25-39
    3. Pages 41-57
    4. Pages 59-69
  3. LCA Groups

    1. Pages 73-79
    2. Pages 81-100
    3. Pages 101-109
    4. Pages 111-126
  4. Noncommutative Groups

    1. Pages 129-140
    2. Pages 149-156
    3. Pages 157-173
  5. Back Matter
    Pages 175-192

About this book


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 T"ubingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. In his leisure time he enjoys hiking in the mountains and practicing Aikido.


Fourier analysis Fourier transform Hilbert space Matrix Riemann integral analysis harmonic analysis set

Authors and affiliations

  1. 1.Department of MathematicsUniversity of ExeterExeter, DevonUK

About the authors

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 practicing Aikido.

Bibliographic information