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.

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...

Table of Contents:

• 1. Introduction
• 2. Harmonic functions on locally compact groups: 2.1. Preliminaries and notation. 2.2. Poisson representation of harmonic functions. 2.3. Semigroup structures of the Poisson space. 2.4. Almost periodic harmonic functions. 2.5. Distal harmonic functions. 2.6. Transitive group actions on Poisson spaces. 2.7. Examples
• 3. Harmonic functionals on Fourier algebras: 3.1. Fourier algebras. 3.2. Harmonic functionals and associated ideals. 3.3. Jordan structures of harmonic functionals. 3.4. Classification of harmonic functionals
• References
• List of symbols
• Index.