調和分析基礎教程（第2版）（英文版） [A First Course in Harmonic analysis] 下載 mobi epub pdf 電子書 2025

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內容簡介

　　Exponentials、The Bessel Inequality、Convergence in the L2-Norm、Uniform Convergence of Fourier Series 、Periodic Functions Revisited、Exercises 等。

內頁插圖

目錄

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 Plancherels 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 Fubinis Theorem
8.3 Convolution
8.4 Plancherels 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

前言/序言

調和分析基礎教程（第2版）（英文版） [A First Course in Harmonic analysis] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

This book is one of the finest maths books I have ever seen. Harmonic analysis is an important field in analysis and is only taught in graduate courses in China. However, this book gives a new view of harmonic analysis and can be readily understood by undergraduate students. In this way, the book has made huge progress in maths education.

評分☆☆☆☆☆

英文版 得好好學英文瞭

評分☆☆☆☆☆

這是一本很好的調和分析的入門書籍，淺顯易懂，觀點較高，一般的大學生從第六章開始讀就可以瞭。

評分☆☆☆☆☆

印刷精美！經典名著！非常值得一看！

評分☆☆☆☆☆

good……

評分☆☆☆☆☆

不錯，很喜歡很實用。要抽時間好好看看。

評分☆☆☆☆☆

差不多

評分☆☆☆☆☆

這是一本很好的調和分析的入門書籍，淺顯易懂，觀點較高，一般的大學生從第六章開始讀就可以瞭。

評分☆☆☆☆☆

入門書。

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