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Non-symmetric translation invariant Dirichlet forms on hypergroups

Bloom, W.R. and Heyer, H. (1987) Non-symmetric translation invariant Dirichlet forms on hypergroups. Bulletin of the Australian Mathematical Society, 36 (1). pp. 61-72.

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In this note translation-invariant Dirichlet forms on a commutative hypergroup are studied. The main theorem gives a characterisation of an invariant Dirichlet form in terms of the negative definite function associated with it. As an illustration constructions of potentials arising from invariant Dirichlet forms are given. The examples of one- and two-dimensional Jacobi hypergroups yield specifications of invariant Dirichlet forms, particularly in the case of Gelfand pairs of compact type.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Cambridge University Press
Copyright: © 1987 Australian Mathematical Society
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