Synopses & Reviews
A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented.
Table of Contents
Preface.- Introduction.- Set-Theoretic Structure.- Topological Structure.- Algebraic Structure.- Combined Topological and Algebraic Structure.- Analysis of Linear Operators (Compact Case).- Analysis of Unbounded Operators.- The Hoelder, Schwartz, and Minkowski Inequalities.- Cardinality.- Zorn's Lemma.- Integration and Measure Theory.- Probability Spaces and Stochastic Processes.- Index of Symbols.- Index.