Harmonic Functions on Groups and Fourier Algebras

  • Authors
  • Cho-Ho Chu
  • Anthony To-Ming Lau

Part of the Lecture Notes in Mathematics book series (LNM, volume 1782)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Cho-Ho Chu, Anthony To-Ming Lau
    Pages 1-4
  3. Cho-Ho Chu, Anthony To-Ming Lau
    Pages 5-50
  4. Cho-Ho Chu, Anthony To-Ming Lau
    Pages 51-89
  5. Cho-Ho Chu, Anthony To-Ming Lau
    Pages 90-97
  6. Cho-Ho Chu, Anthony To-Ming Lau
    Pages 98-100
  7. Back Matter
    Pages 101-105

About this book

Introduction

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.

Keywords

Fourier algebra Harmonic function Jordan algebra Locally compact group Natural Semigroup algebra classification commutative property function functional functions group group action presentation

Bibliographic information

  • DOI https://doi.org/10.1007/b83280
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43595-2
  • Online ISBN 978-3-540-47793-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book