J Austral Math Soc Ser A 50 pp417--467, 1991.

Factorization of Probability Measures on Symmetric Hypergroups

Michael Voit

Abstract

Generalizing known results for special examples, we derive a Khintchine type decomposition of probability measures on symmetric hypergroups. This result is based on a triangular central limit theorem and a discussion of conditions ensuring that the set of all factors of a probability measure is weakly compact. By our main result, a probability measure satisfying certain restrictions can be written as a product of indecomposable factors and a factor in I₀(K), the set of all measures having decomposable factors only. Some contributions to the classification of I₀(K) are given for general symmetric hypergroups and applied to several families of examples like finite symmetric hypergroups and hypergroup joins. Furthermore, all results are discussed in detail for a class of countable compact hypergroups, for Sturm-Liouville hypergroups on [0, ¥] and finally, for polynomial hypergroups.

1980 AMS Subject Classification (1985 Revision): 60B15, 60E07, 60E10, 33A65

Browse the article

Authors

Michael Voit

Mathematisches Institut, Technische Universität München, Arcisstr. 21, D-8000 München 2, Germany.