現代數學物理方法（第1捲） pdf epub mobi txt 電子書 下載 2025

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M.Reed，B.Simon 編

齣版社： 世界圖書齣版公司

ISBN：9787506259316

版次：1

商品編碼：10914222

包裝：平裝

開本：24開

齣版時間：2003-06-01

頁數：400

內容簡介

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.

目錄

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

評分☆☆☆☆☆

這套書很不錯，印刷質量好，內容也詳實，值得認真學習！

評分☆☆☆☆☆

還可以的啊還可以的啊

評分☆☆☆☆☆

專業人士使用。。。。。。。。。。

評分☆☆☆☆☆

數學味比較濃。講的比國內課本多很多。

評分☆☆☆☆☆

經典數學物理教材，70年代就齣版瞭，到現在多次再版，還是常售不衰。這本是第一捲，泛函分析，不知道和Rudin和Stein有什麼區彆。

評分☆☆☆☆☆

上課要用。還好，內容豐富，可以當字典用。

評分☆☆☆☆☆

一直沒時間看，下次找個時間再看

評分☆☆☆☆☆

很經典的一本教材，好好學一下

評分☆☆☆☆☆

非常好的書！