内容简介:
本书由在国际上享有盛誉的普林斯顿大学教授Stein撰写而成，是一部傅立叶分析的入门教材，理论与实践并重。为了便于非数学专业的学生学习，全书内容简明、易懂。全书分为3部分：第1部分介绍傅立叶级数的基本理论及其在等周不等式和等分布中的应用；第2部分研究傅立叶变换及其在经典偏微分方程及Radom变换中的应用；第3部分研究有限阿贝尔群上的傅立叶分析。书中各章均有练习题及思考题。
作者简介:
作者Stein在国际上享有盛誉，现任美国普林斯顿大学数学系教授，是当代分析，特别是调和分析领域领袖人物之一。1974年被选为美国国家科学院院士，1982年被选为美国文理学院院士，1984年获美国数学会的Steele奖，1993年获得瑞士科学院颁发的Stchock奖，1999年获得世界性Wolf数目录:
Foreword
Preface
Chapter 1. The Genesis of Fourier Analysis
1 The vibrating string
2 The heat equation
3 Exercises
4 Problem
Chapter 2. Basic Properties of Fourier Series
1 Examples and formulation of the problem
2 Uniqueness of Fourier series
3 Convolutions
4 Good kernels
5 Cesaro and Abel summability：applications to Fourier series6 Exercises
7 Problem Foreword
Preface
Chapter 1. The Genesis of Fourier Analysis
1 The vibrating string
2 The heat equation
3 Exercises
4 Problem
Chapter 2. Basic Properties of Fourier Series
1 Examples and formulation of the problem
2 Uniqueness of Fourier series
3 Convolutions
4 Good kernels
5 Cesaro and Abel summability：applications to Fourier series6 Exercises
7 Problem
Chapter 3. Covergence of Fourier Series
1 Mean-square convergence of Fourier Series
2 Return to Pointwise Convergence
3 Exercises
4 Problem
Chapter 4. Some Applications of Fourier Series
1 The isoperimetric inequality
2 Weyl's equidistribution theorem
3 A Continuous but nowhere differentiable function
4 The heat equation on the circle
5 Exercises
7 Problems
Chapter 5. The Fourier Transform on R
1 Elementary theory of the Fourier transform
2 Applictions to some partial differential equations
3 The poisson summation formula
4 The Heisenberg uncertainty principle
5 Exercises
6 Problems
Chapter 6. The Fourier Transform on Rd
1 Preliminaries
2 Elementary of the Fourier transform
3 The wave equation in Rd×R
……
Chapter 7 Finite Fourier Analysis
Chapter 8 Dirichlet's Theorem
Appendix: Integration
Notes and References
Bibliography
Symbol Glossary
