线性泛函分析

    本书以较小的篇幅介绍了线性泛函分析的基本内容：赋范空间和Banach空间，内积空间和Hilbert空间，线性算子，紧算子及其在积分方程和微分方程中的应用。本书内容深入浅出、通俗易懂，重要的概念和定理均有背景介绍，并配有简单例子加以解释；排版层次分明、结构清晰；书的末尾配有习题解答。
本书适合大学高年级学生以及研究生自学或作为教材使用。

1 Preliminaries
1.1 Linear Algebra
1.2 Metric Spaces
1.3 Lebesgue Integration
2 Normed Spaces
2.1 Examples of Normed Spaces
2.2 Finite-dimensional Normed Spaces
2.3 Banach Spaces
3 Inner Product Spaces.Hibert Spaces
3.1 Inner Products
3.2 Orthogonality
3.3 Orthogonal Complements
3.4 Orthonormal Bases in Infiniate Dimensions
3.5 Fourier series
4 Linear Operators
4.1 Continuous Linear Transformaations
4.2 The Norm of a Bounded Linear Operator
4.3 The Space and Dual Spaces
4.4 Inverses of Operators
5 Linear Operators on Hilbert Spaces
5.1 The Adjoint of an Operator
5.2 Normal Self-adjoint and Unitary Operators
5.3 The Spectrum of an Operator
……
6 Compact Operators
7 Integral and Differential Equations
8 Solutions to Exercises
Furthe Reading
References
Notation Index
Index

This book provides an introduction to the ideas and methods of linear functional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the theory of metric spaces). . Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equations. Often, the appropriate setting turned out to be a vec..