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Harmonic Functions on Groups and Fourier Algebras

  • Book
  • © 2002

Overview

Authors:
  1. Cho-Ho Chu
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  2. Anthony To-Ming Lau
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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    • Cho-Ho Chu, Anthony To-Ming Lau
    Pages 1-4

  3. Harmonic functions on locally compact groups

    • Cho-Ho Chu, Anthony To-Ming Lau
    Pages 5-50

  4. Harmonic functions on Fourier algebras

    • Cho-Ho Chu, Anthony To-Ming Lau
    Pages 51-89

  5. References

    • Cho-Ho Chu, Anthony To-Ming Lau
    Pages 90-97

  6. List of symbols and Subject Index

    • Cho-Ho Chu, Anthony To-Ming Lau
    Pages 98-100

  7. Back Matter

    Pages 101-105
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Keywords

About this book

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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