本书由世界图书出版公司出版，主要内容包括：Exponentials、The Bessel Inequality、Convergence in the L2-Norm、Uniform Convergence of Fourier Series 、Periodic Functions Revisited、Exercises 等。

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 2-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

7.2 PontryaginDuality

7.3 Exercises

 8 Plancherel Theorem

8.1 Haar Integration

8.2 Fubini's Theorem

8.3 Convolution

8.4 Plancherel's Theorem

8.5 Exercises

Ⅲ Noncommutative Groups

 9 Matrix Groups

9.1 GLn(C) and U(n)

9.2 Representations

9.3 The Exponential

9.4 Exercises

 10 The Representations of SU(2)

10.1 The Lie Algebra

10.2 The Representations

10.3 Exercises

 11 The Peter-Weyl Theorem

11.1 Decomposition of Representations

11.2 The Representation on Hom(Vr,VT)

11.3 The Peter-Weyl Theorem

11.4 AReformulation

11.5 Exercises

 12 The Heisenberg Group

12.1 Definition

12.2 The Unitary Dual

12.3 Hilbert-Schmidt Operators

12.4 The Plancherel Theorem for H

12.5 AReformulation

12.6 Exercises

A TheRiemannZetaFunction

B Haar Integration

Bibiliography

Index