04539nam 22008535 450 991014494260332120200705162802.03-540-47793-410.1007/b83280(CKB)1000000000233258(SSID)ssj0000323728(PQKBManifestationID)12072469(PQKBTitleCode)TC0000323728(PQKBWorkID)10300462(PQKB)10252798(DE-He213)978-3-540-47793-8(MiAaPQ)EBC6286233(MiAaPQ)EBC5610471(Au-PeEL)EBL5610471(OCoLC)1078997946(PPN)155183095(EXLCZ)99100000000023325820121227d2002 u| 0engurnn|008mamaatxtccrHarmonic Functions on Groups and Fourier Algebras /by Cho-Ho Chu, Anthony To-Ming Lau1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (VII, 100 p.) Lecture Notes in Mathematics,0075-8434 ;1782Includes index.3-540-43595-6 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.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.Lecture Notes in Mathematics,0075-8434 ;1782Harmonic analysisPotential theory (Mathematics)Integral equationsTopological groupsLie groupsFunctional analysisFunctions of complex variablesAbstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Potential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Integral Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12090Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Several Complex Variables and Analytic Spaceshttps://scigraph.springernature.com/ontologies/product-market-codes/M12198Harmonic 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.515.53Chu Cho-Hoauthttp://id.loc.gov/vocabulary/relators/aut66924Lau Anthony To-Mingauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144942603321Harmonic Functions on Groups and Fourier Algebras2543727UNINA