Harmonic Functions on Groups and Fourier Algebras

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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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.

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

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