傅里叶分析与小波分析导论(英文版)/经典原版书库

本书是由一位成功的数学家用传统的表述形式编写的教材，除了主要介绍傅里叶级数和傅里叶分析外，还讨论了另一类可以通过傅里叶方法进行研究的正交级数，即小波分析。 本书可以作为理工类专业高年级本科生和低年级研究生的教材。 本书特点： ·书中的所有命题、引理、定理和推论都给出了严格的证明 ·某些情况下，对于一个给定的命题，给出几种证明方法，使学生可以对不同方法进行比较 ·不属于傅里叶分析主流题材但与本书有特定联系的论题，在带有*号的小节中讲述 ·理论和实践相结合

1 FOURIER SERIES ON THE CIRCLE
1. 1 Motivation and Heuristics
1. 1. 1 Motivation from Physics
1. 1. 1. 1 The Vibrating String
1. 1. 1. 2 Heat Flow in Solids
1. 1. 2 Absolutely Convergent Trigonometric Series
1. 1. 3 *Examples of Factorial and Bessel Functions
1. 1. 4 Poisson Kernel Example
1. 1. 5 *Proof of Laplace's Method
1. 1. 6 *Nonabsolutely Convergent Trigonometric Series
1. 2 Formulation of Fourier Series
1. 2. 1 Fourier Coefficients and Their Basic Properties
1. 2. 2 Fourier Series of Finite Measures
1. 2. 3 *Rates of Decay of Fourier Coefficients
1. 2. 3. 1 Piecewise Smooth Functions
1. 2. 3. 2 Fourier Characterization of Analytic Functions
1. 2. 4 Sine Integral
1. 2. 4. 1 Other Proofs That Si( ) =l
1. 2. 5 Pointwise Convergence Criteria

To my parents, Hany A. Pinsky and Helen M. Pinsky, who led me to the path of learning This book provides a self-contained treatment of classical Fourier analysis at the upper undergraduate or begining graduate level. I assume that the reader is familiar with the rudiments of Lebesgue measure and integral on the real line. My viewpoint is mostly classical and concrete, preferring explicit calculations to existential arguments. In some cases. several different proofs are offered for a given proposition to compare different m..