Harmonic Functions on Groups and Fourier Algebras

✍ Scribed by Cho-Ho Chu, Anthony To-Ming Lau (auth.)

• Book ID: 127403415
• Publisher: Springer
• Year: 2002
• Tongue: English
• Weight: 789 KB
• Edition: 1
• Category: Library
• City: Berlin; New York
• ISBN: 3540477934
• ISSN: 0075-8434
• DOI: 10.1007/b83280

✦ Synopsis

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.

✦ Subjects

Several Complex Variables and Analytic Spaces