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Positive definite and related functions on hypergroups

Bloom, W.R. and Ressel, P. (1991) Positive definite and related functions on hypergroups. Canadian Journal of Mathematics, 43 (2). pp. 242-254.

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Abstract

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.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Canadian Mathematical Society
Copyright: © 1991 Canadian Mathematical Society.
URI: http://researchrepository.murdoch.edu.au/id/eprint/31345
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