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Non-symmetric translation invariant Dirichlet forms on hypergroups

Published online by Cambridge University Press:  17 April 2009

Walter R. Bloom  and
Herbert Heyer
Walter R. Bloom
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Perth, Western Australia 6150, Australia
Herbert Heyer
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D–7400 Tübingen 1, Federal Republic of Germany.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 1 , August 1987 , pp. 61 - 72
Copyright
Copyright © Australian Mathematical Society 1987

References

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