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Continuity of convolution semigroups on hypergroups

Bloom, W.R. and Heyer, H. (1988) Continuity of convolution semigroups on hypergroups. Journal of Theoretical Probability, 1 (3). pp. 271-286.

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Let K be a commutative hypergroup with the property that either the identity character is contained in the support of the Plancherel measure on K^, or the identity character is not isolated in K^ and all characters sufficiently close (but not equal) to the identity character vanish at infinity. We present a shift compactness theorem for K and use this to prove that every symmetric convolution semigroup of probability measures on K is continuous.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Plenum Publishing
Copyright: © 1988 Plenum Publishing Corporation
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