Harmonic Functions on Groups and Fourier Algebras

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...

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Bibliographic Details
Main Authors Chu, Cho-Ho, Lau, Anthony To-Ming
Format eBook
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin / Heidelberg 2004
Springer Berlin Heidelberg
Edition1
SeriesLecture Notes in Mathematics
Subjects
Abstract Harmonic Analysis
Differential equations, partial
Functional Analysis
Harmonic analysis
Harmonic functions
Integral Equations
Mathematics
Mathematics and Statistics
Potential Theory
Potential theory (Mathematics)
Several Complex Variables and Analytic Spaces
Topological Groups
Topological Groups, Lie Groups
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Summary: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.
ISBN:3540435956
9783540435952
3662200252
9783662200254
ISSN:0075-8434
1617-9692
DOI:10.1007/b83280