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

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

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

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

评分☆☆☆☆☆

数学味比较浓。讲的比国内课本多很多。

评分☆☆☆☆☆

不错

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☆☆☆☆☆

值得一读的参考书

评分☆☆☆☆☆

好评！好评！好评！好评！好评！好评！

评分☆☆☆☆☆

本书在分析大家Folland的著名实分析名著的泛函分机基础一章中被推荐。可见本书的水平之高。

评分☆☆☆☆☆

很好的书，就是字有些小

评分☆☆☆☆☆

很不错的书，值得购买。

评分☆☆☆☆☆

还没看，双11买的。为了一本书买了很大一堆 。慢慢看。。。

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