Essential Results of Functional Analysis

Name: Essential Results of Functional Analysis
Price: 31.06 USD
Availability: InStock
ISBN: 9780226983387

ISBN-10: 0226983382

ISBN-13: 9780226983387

Edition: 1990

Authors: Robert J. Zimmer

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Description:

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…

Book details

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


6.3



A spectral theorem for elliptic operators


Index