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9783540435952

Harmonic Functions on Groups and Fourier Algebras

by ;
  • ISBN13:

    9783540435952

  • ISBN10:

    3540435956

  • Format: Paperback
  • Copyright: 2002-07-01
  • Publisher: Springer Verlag
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Supplemental Materials

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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.

Table of Contents

Introduction
1(4)
Harmonic functions on locally compact groups
5(46)
Preliminaries and notation
6(5)
Poisson representation of harmonic functions
11(14)
Semigroup structures of the Poisson space
25(6)
Almost periodic harmonic functions
31(8)
Distal harmonic functions
39(4)
Transitive group actions on Poisson spaces
43(3)
Examples
46(5)
Harmonic functionals on Fourier algebras
51(39)
Fourier algebras
52(2)
Harmonic functionals and associated ideals
54(9)
Jordan structures of harmonic functionals
63(19)
Classification of harmonic functionals
82(8)
References 90(8)
List of symbols 98(1)
Index 99

Supplemental Materials

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