A first course in harmonic analysis谐波分析的第一课程
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作者： Anton Deitmar著
出 版 社：
出版时间： 2005-3-1字数：版次： 1页数： 192印刷时间： 2005/03/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387228372包装： 平装编辑推荐
作者简介
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.
内容简介
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.
目录
Ⅰ Fourier Analysis
1 Fourier Series
1.1 Periodic Functions
1.2 Exponentials
1.3 The Bessel Inequality
1.4 Convergence in the L2-Norm
1.5 Uniform Convergence of Fourier Series
1.6 Periodic Functions Revisited
1.7 Exercises
2 Hilbert Spaces
2.1 Pre-Hilbert and Hilbert Spaces
2.2 l2-Spaces
2.3 Orthonormal Bases and Completion
2.4 Fourier Series Revisited
2.5 Exercises
3 The Fourier Transform
3.1 Convergence Theorems
3.2 Convolution
3.3 The Transform
3.4 The Inversion Formula
3.5 Plancherel's Theorem
3.6 The Poisson Summation Formula
3.7 Theta Series
3.8 Exercises
4 Distributions
4.1 Definition
4.2 The Derivative of a Distribution
4.3 Tempered Distributions
4.4 Fourier Transform
4.5 Exercises
Ⅱ LCA Groups
5 Finite Abelian Groups
5.1 The Dual Group
5.2 The Fourier Transform
5.3 Convolution
5.4 Exercises
6 LCA Groups
6.1 Metric Spaces and Topology
6.2 Completion
6.3 LCA Groups
6.4 Exercises
7 The Dual Group
7.1 The Dual as LCA Group
……
8 Plancherel Theorem
Ⅲ Noncommutative Groups
10 The Representations of SU（2）
11 The Peter -Weyl Theorem
12 .The Heisenberg Group
A The Riemann Zeta Function
B Haar Integration
Bibiliography
Index
