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Elements of Functional Analysis - I.J. Maddox

Elements of Functional Analysis

Paperback

Published: 27th March 1989
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The second edition of this successful textbook, first published in 1970, retains the aims of the first, namely to provide a truly introductory course in functional analysis, but the opportunity has been taken to add more detail and worked examples. The main changes are complete revisons of the work on convex sets, metric and topological linear spaces, reflexivity and weak convergence. Additional material on the Weiner algebra of absolutely convergent Fourier series and on weak topologies is included. A final chapter includes elementary applications of functional analysis to differential and integral equations.

Preface to the second edition
Preface to the first edition
Basic Set Theory and Analysis
Sets and functions
Real and complex numbers
Sequences of functions, continuity, differentiability
Inequalities
Metric and Topological Spaces
Metric and semimetric spaces
Complete metric spaces
Some metric and topological concepts
Continuous functions on metric and topological spaces
Compact sets
Category and uniform boundedness
Linear and Linear Metric Spaces
Linear spaces
Subspaces, dimensionality, factorspaces, convex sets
Metric linear spaces, topological linear spaces
Basis
Normed Linear Spaces
Convergence and completeness
Linear operators and functionals
The Banach-Steinhaus theorem
The open mapping and closed graph theorems
The Hahn-Banach extension
Weak topology and weak convergence
Algebras and Banach algebras
Homomorphisms and isomorphisms
The spectrum and the Gelfand-Mazaur theorem
The Weiner algebra
Hilbert Space
Inner product and Hilbert spaces
Orthonormal sets
The dual space of a Hilbert space
Symmetric and compact operators
Applications
Differential and integral problems
The Sturm-Liouville problem
Matrix transformations in sequence spaces
Appendix
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521358682
ISBN-10: 052135868X
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 256
Published: 27th March 1989
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.78 x 15.06  x 1.58
Weight (kg): 0.37
Edition Number: 2
Edition Type: Revised