Harmonic Functions on Groups and Fourier Algebras : Lecture Notes in Mathematics - Cho-Ho Chu

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Harmonic Functions on Groups and Fourier Algebras

By: Cho-Ho Chu, Anthony To-Ming Lau

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Paperback | 1 July 2002

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116 Pages

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24.13 x 15.24 x 1.27

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This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Topology Calculus & Mathematical Analysis Differential Calculus & Equations Functional Analysis & Transforms Complex Analysis

Introduction	p. 1
Harmonic functions on locally compact groups	p. 5
Preliminaries and notation	p. 6
Poisson representation of harmonic functions	p. 11
Semigroup structures of the Poisson space	p. 25
Almost periodic harmonic functions	p. 31
Distal harmonic functions	p. 39
Transitive group actions on Poisson spaces	p. 43
Examples	p. 46
Harmonic functionals on Fourier algebras	p. 51
Fourier algebras	p. 52
Harmonic functionals and associated ideals	p. 54
Jordan structures of harmonic functionals	p. 63
Classification of harmonic functionals	p. 82
References	p. 90
List of symbols	p. 98
Index	p. 99
Table of Contents provided by Publisher. All Rights Reserved.

Harmonic Functions on Groups and Fourier Algebras

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