Harmonic Functions on Groups and Fourier Algebras. Anthony To-Ming Lau, Cho-Ho Chu

Harmonic Functions on Groups and Fourier Algebras



Download Harmonic Functions on Groups and Fourier Algebras



Harmonic Functions on Groups and Fourier Algebras Anthony To-Ming Lau, Cho-Ho Chu. djvu ebook
Publisher: Springer
Language: English
Page: 107
ISBN: 3540435956, 9783540435952

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.



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