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Essential Results of Functional Analysis

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ISBN-10: 0226983382

ISBN-13: 9780226983387

Edition: 1990

Authors: Robert J. Zimmer

List price: $22.50
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Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed…    
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Book details

List price: $22.50
Copyright year: 1990
Publisher: University of Chicago Press
Publication date: 1/15/1990
Binding: Paperback
Pages: 168
Size: 5.50" wide x 8.25" long x 0.25" tall
Weight: 0.396
Language: English

Preface 0
Background 0
Review of basic functional analysis 0
Some special properties of integration in Rn
Topological vector spaces and operators
Examples of spaces
Examples of operators
Operator topologies and groups of operators
Convexity and fixed point theorems
Kakutani-Markov fixed point theorem
Haar measure for compact groups
Krein-Millman theorem
Compact operators
Compact operators and Hilbert-Schmidt operators
Spectral theorem for compact normal operators
Peter-Weyl theorem for compact groups
General spectral theory
Spectrum of an operator
Spectral theorem for self-adjoint operators
Gelfand's theory of commutative C*-algebras
Mean ergodic theorem
Fourier transforms and Sobolev embedding theorems
Basic properties of the Fourier transform and the Plancherel theorem
Sobolev and Rellich embedding theorems
Distributions and elliptic operators
Basic properties of distributions
Distributions and Sobolev spaces
Regularity for elliptic operators
Appendix to
A spectral theorem for elliptic operators