M·Reed《现代数学物理方法(第1卷)》

M·Reed《现代数学物理方法(第1卷)》

作者:M·Reed

出版社:世界图书出版公司

出版年:2003-6

评分:7.9

ISBN:9787506259316

所属分类:教辅教材

书刊介绍

内容简介

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作品目录

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

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