A First Course in Harmonic Analysis [Hardcover]

Anton Deitmar (Author)

Book Description

ISBN-10: 0387953752 | ISBN-13: 978-0387953755 | Publication Date: February 22, 2002 | Edition: 1

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.

Editorial Reviews

Review

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)

From the Back Cover

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. --This text refers to the Paperback edition.

See all Editorial Reviews

Product Details

• Hardcover: 168 pages
• Publisher: Springer; 1 edition (February 22, 2002)
• Language: English
• ISBN-10: 0387953752
• ISBN-13: 978-0387953755
• Product Dimensions: 9.6 x 6.4 x 0.6 inches
• Shipping Weight: 14.2 ounces
• Amazon Best Sellers Rank: #4,139,823 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.