现代数学物理方法（第1卷） 下载 mobi epub pdf 电子书 2024

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内容简介

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modem physics, and partial differenrial equations.

目录

Preface
Introduction
Contents of Other Volumes
I: PRELIMINARIES
1. Sets and functions
2. Metric and normed linear spaces
Appendix Lira sup and lim inf
3. The Lebesgue integral
4. Abstract measure theory
5. Two conrergence arguments
6. Equicontinuity
Notes
Problems

II: HILBERT SPACES
1. The geometry of Hilbert space
2. The Riesz lemma
3. Orthonormal bases
4. Tensor products of Hilbert spaces
5. Ergodic theory: an introduction
Notes
Problems

III: BANACH SPACES
1. Definition and examples
2. Duals and double duals
3. The Hahn-Banach theorem
4. Operations on Banach spaces
5. The Baire category theorem and its consequences
Notes
Problems
IV: TOPOLOGICAL SPACES
1. General notions
2. Nets and Convergence
3. Compactness
Appendix The Stone-Weierstrass theorem
4. Measure theory on Compact spaces
5. Weak topologies on Banach spaces
Appendix Weak and strong measurability
Notes
Problems


V: LOCALLY ONVEX SPACES
1. General properties
2. Frdchet spaces
3. Functions of rapid decease and the tempered distributions
Appendix The N-representation for and
4. Inductive limits: generalized functions and weak solutions of partial differential equations
5. Fixed point theorems
6. Applications of fixed point theorems
7. Topologies on locally convex spaces: duality theory and the strong dual topology
Appendix Polars and the Mackey-Arens theorem
Notes
Problems
VI: BOUNDED OPERATORS
VII: THE SPECTRAL THEOREM
VIII: UNBOUNDED OPERATORS
THE FOURIER TRANSFORM
SUPPLEMENTARY MATERIAL
List of Symbols

前言/序言

现代数学物理方法（第1卷） 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

泛函经典之作，印刷还好

评分☆☆☆☆☆

物理用泛函，这个形容差不多吧，个人看法，勿撕。

评分☆☆☆☆☆

经典数学物理教材，70年代就出版了，到现在多次再版，还是常售不衰。这本是第一卷，泛函分析，不知道和Rudin和Stein有什么区别。

评分☆☆☆☆☆

讲解清晰，内容专业，理论系统，值得推荐！

评分☆☆☆☆☆

物超所值，没有见过这么便宜的货了！

评分☆☆☆☆☆

讲解清晰，内容专业，理论系统，值得推荐！

评分☆☆☆☆☆

先买了两本，希望下次折的力度大些

评分☆☆☆☆☆

很经典的一本教材，好好学一下

评分☆☆☆☆☆

帮人买的，有点小贵，还行

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