《泛函分析（影印版）》

《泛函分析（影印版）》 内容介绍：

《泛函分析(影印版)》是美国科学院院士Peter D．Lax在CotJrant数学所长期讲授泛函分析课程的教学经验基础上编写的。《泛函分析(影印版)》包括泛函分析的基本内容：Barlach空间、Hilbert空间和线性拓扑空间的基本概念和性质，线性拓扑空间中的凸集及其端点集的性质，有界线性算子的性质等。可作为本科生泛函分析课的教学内容；还包括泛函分析较深的内容：自伴算子的谱分解理论。紧算子的理论，交换Barlach代数的Gelfand理论，不变子空间的理论等。可作为研究生泛函分析课的教学内容。《泛函分析(影印版)》特别强调泛函分析与其他数学分支的联系及泛函分析理论的应用，可以使读者深刻地理解到：抽象的泛函分析理论有着丰富的数学背景。

《泛函分析（影印版）》 目录大纲：

Foreword
1.Linear Spaces
2.Linear Maps
3.The Hahn-Banach Theorem
4.Applications of the Hahn-Banach theorem
5.Normed Linear Spaces
6.Hilbert Space
7.Applications of Hilbert Space Results
8.Duals of Normed Linear Speaces
9.Applications of Duality
10.Weak Convergence
11.Applications of Weak Convergence
12.The Weak and Weak Topologies
13.Locally Convex Topologies and the Krein-Milman Theorem
14.Examples of Convex Sets and Their Extreme Points
15.Bounded Linear Maps
16.Examples of Bounded Linear Maps
17.Banach Algebras and their Elementary Spectral Theory
18.Gelfand's Theory of Commutative Banach Algebras
19.Applications of Gelfand's Theory of Commutative Banach Algebras
20.Examples of Operators and Their Spectra
21.Compact Maps
22.Examples of Compact Operators
23.Positive compact operators
24.Fredholm's Theory of Integral Equations
25.Invariant Subspaces
26.Harmonic Analysis on a Halfline
27.Index Theory
28.Compact Symmetric Operators in Hilbert Space
29.Examples of Compact Sysmmetric Operators
30.Trace Class and Trace Formula
31.Spectral Theory of Symmetric,Normal,and Unitary Operators
32.Spectral Theory of Self-Adjoint Operators
33.Examples of Self-Adjoint Operators
34.Semigroups of Operators
35.Groups of Unitary Operators
36.Examples of Strongly Continuous Semigroups
37.Scattering Theory
38.A Theorem of Beurling
A.Riesz-Kakutani representation theorem
B.Theory of distrbutions
C.Zorn's Lemma
Author Index
Subject Index