Preface
About the Author
PartⅠ General Theory
1 Topological Vector Spaces
Introduction
Separation properties
Linear mappings
Finite-dimensional spaces
Metrization
Boundedness and continuity
Seminorms and local convexity
Quotient spaces
Examples
Exercises
2 Completeness
Baire category
The Banach-Steinhaus theorem
The open mapping theorem
The closed graph theorem
Bilinear mappings
Exercises
3 Convexity
The Hahn-Banach theorems
Weak topologies
Compact convex sets
Vector-valued integration
Holomorphic functions
Exercises
4 Dualityin Banach Spaces
The normed dual of a normed space
Adjoints
Compact operators
Exercises
5 Some Applications
A continuity theorem
Closed subspaces of LP-spaces
The range of a vector-valued measure
A generalized Stone-Weierstrass theorem
Two interpolation theorems
Kakutani's fixed point theorem
Haar measure on compact groups
Uncomplemented subspaces
Sums of Poisson kernels
Two more fixed point theorems
Exercises
PartⅡ Distributions and Fourier Transforms
6 Test Functions and Distributions
Introduction
Test function spaces
Calculus with distributions
Localization
Supports of distributions
Distributions as derivatives
Convolutions
Exercises
7 Fourier Transforms
Basic properties
Tempered distributions
Paley-Wiener theorems
Sobolev's lemma
Exercises
8 Applications to Differential Equations
Fundamental solutions
Elliptic equations
Exercises
……
Part Ⅲ Banach Algebras and Spectral Theory
Appendix A Compactness and Continuity
Appendix B Notes and Comments
Bibliography
List of Special Symbols
Index
鄂公网安备 42010302001612号 