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100   $a20121227d2002      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aHarmonic Functions on Groups and Fourier Algebras$b[electronic resource] /$fby Cho-Ho Chu, Anthony To-Ming Lau
205   $a1st ed. 2002.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002.
215   $a1 online resource (VII, 100 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1782
300   $aIncludes index.
311   $a3-540-43595-6 
327   $a1. 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.
330   $aThis research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1782
606   $aHarmonic analysis
606   $aPotential theory (Mathematics)
606   $aIntegral equations
606   $aTopological groups
606   $aLie groups
606   $aFunctional analysis
606   $aFunctions of complex variables
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163
606   $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090
606   $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198
615  0$aHarmonic analysis.
615  0$aPotential theory (Mathematics).
615  0$aIntegral equations.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aFunctional analysis.
615  0$aFunctions of complex variables.
615 14$aAbstract Harmonic Analysis.
615 24$aPotential Theory.
615 24$aIntegral Equations.
615 24$aTopological Groups, Lie Groups.
615 24$aFunctional Analysis.
615 24$aSeveral Complex Variables and Analytic Spaces.
676   $a515.53
700   $aChu$b Cho-Ho$4aut$4http://id.loc.gov/vocabulary/relators/aut$066924
702   $aLau$b Anthony To-Ming$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466603203316
996   $aHarmonic Functions on Groups and Fourier Algebras$92543727
997   $aUNISA