泛函分析（英文版第2版）（美）Walter Rudin|15906 下载 mobi epub pdf 电子书 2024

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发表于2024-05-09

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店铺：互动出版网图书专营店

出版社：机械工业出版社

ISBN：711113415x

商品编码：1245556866

丛书名：经典原版书库

出版时间：2003-12-01

页数：424

图书描述

书[0名0]：	泛函分析（英文版 [0第0]2版）\|15906
图书定价：	42元
图书作者：	（美）Walter Rudin
出版社：	机械工业出版社
出版日期：	2003/12/1 0:00:00
ISBN号：	711113415x
开本：	16开
页数：	424
版次：	1-1

内容简介

　　泛函分析是分析数[0学0]中“年轻”的分支，在各个[0领0]域均有着广泛应用。本书是泛函分析的经典教材。作为Rudin的分析[0学0]经典著作之一，本书秉承了内容精练、结构清晰的特点。[0第0]2版新增的内容有Kakutani不动点定理、Lamo[0no0]sov不变子空间定理以及遍历定理等。另外，还适[0当0]增加了一些例子和习题。

Preface
Part I General Theory
1 Topological Vector Spaces
Introduction
Separation properties
Linear mappings
Finite-dimensional spaces
Metrization
Boundedness and continuity
Semi[0no0]rms and local convexity
Quotient spaces
Examples
Exercises
Completeness
Baire category
The Banach-Steinhaus theorem
The open mapping theorem
The closed graph theorem
Bilinear mappings
Exercises
3 Convexity
The Hahn-Banach theorems
Weak topologies
Compact convex sets
Vector-valued integration
Holomorphic functions
Exercises
4 Duality in Banach Spaces
The [0no0]rmed dual of a [0no0]rmed space
Ad joints
Compact operators
Exercises
5 Some Appl_ications
A continuity theorem
Closed subspaces of LP-spaces
The range of a vector-valued measure
A generalized Stone-Weierstrass theorem
Two interpolation theorems
Kakutani's fixed point theorem
Haar measure on compact groups
Uncomplemented subspaces
Sums of Poisson kernels
Two more fixed point theorems
Exercises
Part II Distributions and Fourier Transforms
6 Test Functions and Distributions
Introduction
Test function spaces
Calculus with distributions
Localization
Supports of distributions
Distributions as derivatives
Convolutions
Exercises
7 Fourier Transforms
Basic properties
Tempered distributions
Paley-Wiener theorems
Sobolev's lemma
Exercises
8 Applications to Differential Equations
Fundamental solutions
Elliptic equations
Exercises
9 Tauberian Theory
Wiener's theorem
The prime number theorem
The renewal equation
Exercises
Part III Banach Algebras and Spectral Theory
10 Banach Algebras
Introduction
Complex homomorphisms
Basic properties of spectra
Symbolic calculus
The group of invertible elements
Lomo[0no0]sov's invariant subspace theorem
Exercises
11 Commutative Banach Algebras
Ideals and homomorphisms
Gelfand transforms
Involutions
Applications to [0no0]ncommutative algebras
Positive functionals
Exercises
12 Bounded Operators on a Hilbert Space
Basic facts
Bounded operators
A commutativity theorem
Resolutions of the identity
The spectral theorem
Eigenvalues of [0no0]rmal operators
Positive operators and square roots
The group of invertible operators
A characterization of B*-algebras
An ergodic theorem
Exercises
13 Unbounded Operators
Introduction
Graphs and symmetric operators
The Cayley transform
Resolutions of the identity
The spectral theorem
Semigroups of operators
Exercises
Appendix A Compactness and Continuity
Appendix B [0No0]tes and Comments
Bibliography
List of Special Symbols
Index

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