Harmonic Functions on Groups and Fourier Algebras
Edition: 1 edition
Publisher: Springer
Published: July 10, 2002
Language: eng
Format: Paperback
Number of pages: 107
ISBN-13: 9783540435952
Subjects: Fourier analysis; Potential Theory; Harmonic Analysis; Topology - General; Mathematics; Science/Mathematics; Mathematical Analysis; Harmonic functions; Calculus; Group Theory; Fourier algebra; Harmonic function; Jordan algebra; Locally compact group; Mathematics / Calculus; Mathematics / Mathematical Analysis; Mathematics-Group Theory; Mathematics-Mathematical Analysis; Banach algebras; Functional Analysis; Locally compact groups
First sentence: Let G be a Lie group and let be the Laplace operator on G.
Description: 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.