Applied Functional Analysis

Author: Hu Shigeng Li Pengqi
Publisher:
Publish Date: 2003-08-01
Features:
Chapter 1 Abstract Spaces
1.1 Banach Spaces
1.2 Function Spaces
1.3 Point Sets and Continuity
1.4 Compactness and Dimension Theorem
1.5 Hilbert Spaces
1.6 Sobolev Spaces
1.7 Other Abstract Spaces
Exercises
Chapter 2 Linear Operators and Linear Functionals
2.1 Bounded Linear Operators
2.2 Common Bounded Linear Operators
2.3 Dual Spaces and Dual Operators
2.4 Fundamental Theorems
2.5 Weak Convergence
Exercises
Chapter 3 Preliminaries of Spectral Theory
3.1 Spectrum of Bounded Linear Operators
3.2 Operator Functions
3.3 Compact Linear Operators
3.4 Bounded Linear Operators on Hilbert Spaces
3.5 Unbounded Operators
Exercises
Chapter 4 Nonlinear Operators and Nonlinear Functionals
4.1 Differential Theory
4.2 Contraction Mapping and Iterative Methods
4.3 Implicit Function Theorem
4.4 Compact Operators
4.5 Convex Functions
4.6 Extremum Theory
Exercises
Exercises and Solutions
References
Index of Terms