Anton Deitmar

A First Course in Harmonic Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book provides an introduction to the central topics and techniques in harmonic analysis. In contrast to the competitive literature available, this book is based on the Riemann integral and metric spaces, in lieu of the Lebesgue integral and abstract topology. This edition has been revised to include two new chapters on distributions and the Heisenberg Group.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 192
• Erscheinungstermin: 24. November 2005
• Englisch
• ISBN-13: 9780387275611
• Artikelnr.: 38189348

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

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 Móricz 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)