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Fourier Analysis and Its Applications, by Gerald B. Folland, first published by the American Mathematical Society. Copyright © 1992 by the American Mathematical Society. All rights reserved.This present reprint edition is published by Higher Education Press Limited Company under authorityof the American Mathematical Society and is published under license. Special Edition for People's Republic of China Distribution Only. This edition has been authorized bythe American Mathematical Society for sale in People's Republic of China only, and is not for export therefrom. 本书原版最初由美国数学会于 1992 年出版，原书名为 Fourier Analysis and Its Applications，作者为 Gerald B. Folland。美国数学会保留原书所有版权。 原书版权声明：Copyright © 1992 by the American Mathematical Society。 本影印版由高等教育出版社有限公司经美国数学会独家授权出版。 本版只限于中华人民共和国境内发行。本版经由美国数学会授权仅在中华人民共和国境内销售，不得出口。

前辅文 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 Orthogonal 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 3.5 Regular Sturm-Liouville 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 Dirichlet 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 5.4 Orthogonal sets of Bessel functions 5.5 Applications of Bessel functions 5.6 Variants of Bessel functions 6 Orthogonal Polynomials 6.1 Introduction 6.2 Legendre polynomials 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-Liouville 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 8.5 Applications: Integral equations 8.6 Asymptotics of Laplace transforms 9 Generalized Functions 9.1 Distributions 9.2 Convergence, convolution, and approximation 9.3 More examples: Periodic distributions and finite parts 9.4 Tempered distributions and Fourier transforms 9.5 Weak solutions of differential equations 10 Green's Functions 10.1 Green's functions for ordinary differential operators 10.2 Green's functions for partial differential operators 10.3 Green's functions and regular Sturm-Liouville problems 10.4 Green's functions and singular Sturm-Liouville problems 1 Some physical derivations 2 Summary of complex variable theory 3 The gamma function 4 Calculations in polar coordinates 5 The fundamental theorem of ordinary differential equations Answers to the Exercises References Index of Symbols Index

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