Harmonic Functions on Groups and Fourier Algebras

• Main Authors: Chu, Cho-Ho (Author, http://id.loc.gov/vocabulary/relators/aut), Lau, Anthony To-Ming (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1782
• Subjects: Harmonic analysis.; Potential theory (Mathematics).; Integral equations.; Topological groups.; Lie groups.; Functional analysis.; Functions of complex variables.; Abstract Harmonic Analysis.; Potential Theory.; Integral Equations.; Topological Groups, Lie Groups.; Functional Analysis.; Several Complex Variables and Analytic Spaces.
• Physical Description: VII, 100 p. online resource.
• ISBN: 9783540477938
• ISSN: 0075-8434 ;
• DOI: 10.1007/b83280

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.