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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

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

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不錯

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還沒看，雙11買的。為瞭一本書買瞭很大一堆 。慢慢看。。。

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這套書很不錯，印刷質量好，內容也詳實，值得認真學習！

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本書在分析大傢Folland的著名實分析名著的泛函分機基礎一章中被推薦。可見本書的水平之高。

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泛函經典之作，印刷還好

評分☆☆☆☆☆

這套書已經經曆瞭將近半個世紀瞭，一直受到PDE的學者的推崇。這本書把當時的量子力學做瞭全麵的描述。

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物理用泛函，這個形容差不多吧，個人看法，勿撕。

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非常好的書，孩子特彆喜歡

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