泛函分析导引（影印版）
作者： Steven G.Krantz
出版时间：2022-02-28
出版社：高等教育出版社
- 高等教育出版社
- 9787040570243
- 1版
- 412514
- 46254232-5
- 精装
- 16开
- 2022-02-28
- 270
- 160
- 理学
- 数学
- 数学类
- 研究生及以上
前辅文
1 Fundamentals
1.1 What is Functional Analysis?
1.2 Normed Linear Spaces
1.3 Finite-Dimensional Spaces
1.4 Linear Operators
1.5 The Baire Category Theorem
1.6 The Three Big Results
1.7 Applications of the Big Three
2 Ode to the Dual Space
2.1 Introduction
2.2 Consequences of the Hahn-Banach Theorem
3 Hilbert Space
3.1 Introduction
3.2 The Geometry of Hilbert Space
4 The Algebra of Operators
4.1 Preliminaries
4.2 The Algebra of Bounded Linear Operators
4.3 Compact Operators
5 Banach Algebra Basics
5.1 Introduction to Banach Algebras
5.2 The Structure of a Banach Algebra
5.3 Ideals
5.4 The Wiener Tauberian Theorem
6 Topological Vector Spaces
6.1 Basic Ideas
6.2 Fr´echet Spaces
7 Distributions
7.1 Preliminary Remarks
7.2 What is a Distribution?
7.3 Operations on Distributions
7.4 Approximation of Distributions
7.5 The Fourier Transform
8 Spectral Theory
8.1 Background
8.2 The Main Result
9 Convexity
9.1 Introductory Thoughts
9.2 Separation Theorems
9.3 The Main Result
10 Fixed-Point Theorems
10.1 Banach’s Theorem
10.2 Two Applications
10.3 The Schauder Theorem
Table of Notation
Glossary
Bibliography
Index
About the Author
