Positive Definite and Related Functions on Hypergroups

In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Lévy-Khinchin representation for negative definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely...

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Bibliographic Details
Published in:Canadian journal of mathematics 1991-04, Vol.43 (2), p.242-254
Main Authors: Bloom, Walter R., Ressel, Paul
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Probability and statistics
Probability theory and stochastic processes
Probability theory on algebraic and topological structures
Sciences and techniques of general use
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Summary:In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Lévy-Khinchin representation for negative definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely alternating functions. The techniques employed here also lead to considerable simplification of the proofs of known results on positive definite and negative definite functions on hypergroups.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-1991-013-2