ENGLISH

Harmonic Functions on Groups and Fourier Algebras

By Cho-Ho Chu , Anthony To-Ming Lau (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2002
ISBN
9783540435952, 3540435956
DOI
10.1007/b83280
ISSN
0075-8434
Open Library ID
OL9057739M
Language
english
Format
PDF
Filesize
820 kB (839663 bytes)
Series
Lecture Notes in Mathematics 1782
Edition
1
Pages
100\107
Time added
2010-02-18 13:16:04
Abstract Harmonic Analysis; Potential Theory; InteLie Groups; Functional Analysis; Several Complex V

Description

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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