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Random Fourier series on compact abelian hypergroups

Part of: Abstract harmonic analysis Stochastic processes

Published online by Cambridge University Press:  09 April 2009

John J. F. Fournier  and
Kenneth A. Ross
John J. F. Fournier
Affiliation:
Department of Mathematics University of British ColumbiaVancouver, CanadaV6T 1Y4
Kenneth A. Ross
Affiliation:
Department of Mathematics University of OregonEugene, Oregeon 97403, U.S.A.
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Abstract

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Random Fourier series are studied for a class of compact abelian hypergroups. The randomizing factors are assumed to be independent and uniformly subgaussian. In the presence of a natural teachnical hypothesis, an entropy condition of Dudley is shown to be sufficient for almost sure continuity. The classical results on almost sure membership in Lp, where p < ∞, are generalized to this setting. As an application, it is shown that a simple condition on the dual object implies that the de Leeuw-Kahane-Katznelson phenomenon occurs. Another application is the analogue of a classical sufficient condition for almost sure continuity. Examples illustrating the general theory are given for the hypergroup of conjugacy classes of SU(2) and for a class of compact countable hypergroups.

Keywords

random Fourier seriesuniformly subgaussian random variablescompact abelian hypergroup.

MSC classification

Secondary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 45 - 81
Copyright
Copyright © Australian Mathematical Society 1984

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