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Negative definite functions and convolution semigroups of probability measure on a commutative hypergroup

Bloom, W.R. and Heyer, H. (1996) Negative definite functions and convolution semigroups of probability measure on a commutative hypergroup. Probability and Mathematical Statistics, 16 (1). pp. 157-176.

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Abstract

Corresponding to the definitions of positive definite functions there are various approaches to defining negative definite functions on hypergroups. These range from the obvious “pointwise” definition to axiomatization via the Schoenberg duality. Researchers in this area have used definitions best suited to their immediate purposes. In this paper we present a comprehensive treatment of negative definite functions on commutative hypergroups, leading to convolution semigroups of probability measures and their Levy-Khintchine representation within the framework of commutative hyper-groups on subsets of Euclidean space.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: WROCŁAW UNIVERSITY OF TECHNOLOGY
URI: http://researchrepository.murdoch.edu.au/id/eprint/31323
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