Fourier分析及其应用(英文版)(精)/美国数学会经典影印系列

本书在适合于高年级本科生学习的水平上讲述 Fourier级数和Fourier积分、特征函数展开以及相关 论题的理论和应用，内容涵盖Bessel函数、正交多项 式和Laplace变换，还包括了对于常微分方程和偏微分 方程的广义函数和Green函数的一些章节。本书几乎专 门处理这些主题的可用于物理和工程中的那些方面， 同时也包含了广泛的各类应用。在理论方面，它使用 现代分析中的思想来展开技术背后的概念和推理，而 叉没有陷入严格证明的技术细节的陷阱中。

1 Overture 1.1 Some equations of mathematical physics 1.2 Linear differential operators 1.3 Separation of variables 2 Fourier Series 2.1 The Fourier series of a periodic function 2.2 A convergence theorem 2.3 Derivatives, integrals, and uniform convergence 2.4 Fourier series on intervals 2.5 Some applications 2.6 Further remarks on Fourier series 3 0rthogonal Sets of Functions 3.1 Vectors and inner products 3.2 Functions and inner products 3.3 Convergence and completeness 3.4 More about L2 spaces; the dominated convergence theorem 3.5 Regular Sturm-LiouviUe problems 3.6 Singular Sturm-Liouville problems 4 Some Boundary Value Problems 4.1 Some useful techniques 4.2 One-dimensional heat flow 4.3 One-dimensional wave motion 4.4 The Dirichlct problem 4.5 Multiple Fourier series and applications 5 Bessel Functions 5.1 Solutions of Bessel's equation 5.2 Bessel function identities 5.3 Asymptotics and zeros of Bessel functions 5.40 rthogonal sets of Bessel functions 5.5 Applications of Bessel functions 5.6 Variants of Bessel functions 6 0rthogonal Polynomials 6.1 Introduction 6.2 Legendrepolynomials 6.3 Spherical coordinates and Legendre functions 6.4 Hermite polynomials 6.5 Laguerre polynomials 6.6 Other orthogonal bases 7 The Fourier Transform 7.1 Convolutions 7.2 The Fourier transform 7.3 Some applications 7.4 Fourier transforms and Sturm-LiouviUe problems 7.5 Multivariable convolutions and Fourier transforms 7.6 Transforms related to the Fourier transform 8 The Laplace Transform 8.1 The Laplace transform 8.2 The inversion formula 8.3 Applications: Ordinary differential equations 8.4 Applications: Partial differential equations