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  • Book
  • © 2002

Harmonic Functions on Groups and Fourier Algebras

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
  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

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.

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

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions