Harmonic Functions on Groups and Fourier Algebras, Issue 1782This 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. |
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Harmonic Functions on Groups and Fourier Algebras Cho-Ho Chu,Anthony To-Ming Lau Limited preview - 2004 |
Harmonic Functions on Groups and Fourier Algebras Cho-Ho Chu,Anthony To-Ming Lau No preview available - 2014 |
Common terms and phrases
action of G adapted algebra amenable AP(G Banach algebra bounded called closed constant contains continuous character contractive projection converges convex hull Ctu(G define denote dense distal dual equicontinuous equivalent Example exists extreme point f x g follows Fourier algebra functions on G G acts transitively G M(G Given gives group action group G harmonic functions Hence homeomorphism idempotent identity implies induces isometry isomorphic Jordan Lemma Let G Ll(G locally compact group means measure on G multiplicative neighbourhood Neumann algebra non-degenerate periodic pointwise Poisson representation Poisson space probability measure Proof properties Proposition Remark restriction result semigroup semigroup structure shown subgroup subnet supp Theorem topology translation invariant uniformly continuous WAP(G weak weak*-topology weakly write x G G
Bibliographic information
| Title | Harmonic Functions on Groups and Fourier Algebras, Issue 1782 Harmonic Functions on Groups and Fourier Algebras, Anthony To-Ming Lau Volume 1782 of Lecture Notes in Mathematics Lecture notes in mathematics Berlin: Mathematical biosciences subseries University of Arkansas lecture notes in mathematics, ISSN 0075-8434 |
| Authors | Cho-Ho Chu, Anthony To-Ming Lau |
| Edition | illustrated |
| Publisher | Springer Science & Business Media, 2002 |
| ISBN | 3540435956, 9783540435952 |
| Length | 100 pages |
| Subjects | › › Mathematics / Calculus Mathematics / Complex Analysis Mathematics / Functional Analysis Mathematics / Group Theory Mathematics / Mathematical Analysis Mathematics / Probability & Statistics / Stochastic Processes Mathematics / Topology Mathematics / Vector Analysis |
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