Overview

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.

Full Product Details

Author:   Anton Deitmar
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd ed. 2005
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.660kg
ISBN:  

9780387228372

ISBN 10:   0387228373
Pages:   192
Publication Date:   09 March 2005
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Fourier Analysis.- Fourier Series.- Hilbert Spaces.- The Fourier Transform.- Distributions.- LCA Groups.- Finite Abelian Groups.- LCA Groups.- The Dual Group.- Plancherel Theorem.- Noncommutative Groups.- Matrix Groups.- The Representations of SU(2).- The Peter-Weyl Theorem.- The Heisenberg Group.

Reviews

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)

From the reviews of the first edition: <p> 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. a ] <p>Sanjiv Kumar Gupta for MathSciNet <p> a ] 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. <p>Ferenc MA3ricz for Acta Scientiarum Mathematicarum <p>From the reviews of the second edition: <p> This is the second edition of a beautiful introduction to harmonic analysis accessible to undergraduates. a ] 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)

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)

"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)"

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)

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)

Author Information

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.

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