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007 cr nn 008mamaa
008 121227s2002 gw | s |||| 0|eng d
020 _a9783540477938
_9978-3-540-47793-8
024 7 _a10.1007/b83280
_2doi
050 4 _aQA403-403.3
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
082 0 4 _a515.785
_223
100 1 _aChu, Cho-Ho.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aHarmonic Functions on Groups and Fourier Algebras
_h[electronic resource] /
_cby Cho-Ho Chu, Anthony To-Ming Lau.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aVII, 100 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1782
505 0 _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.
520 _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.
650 0 _aHarmonic analysis.
650 0 _aPotential theory (Mathematics).
650 0 _aIntegral equations.
650 0 _aTopological Groups.
650 0 _aFunctional analysis.
650 0 _aDifferential equations, partial.
650 1 4 _aAbstract Harmonic Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12015
650 2 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
650 2 4 _aIntegral Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12090
650 2 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aSeveral Complex Variables and Analytic Spaces.
_0http://scigraph.springernature.com/things/product-market-codes/M12198
700 1 _aLau, Anthony To-Ming.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662200254
776 0 8 _iPrinted edition:
_z9783540435952
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1782
856 4 0 _uhttps://doi.org/10.1007/b83280
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10735
_d10735