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Positive Definite and Related Functions on Hypergroups

Published online by Cambridge University Press:  20 November 2018

Walter R. Bloom and
Paul Ressel
Walter R. Bloom
Affiliation:
School of Mathematical and Physical Sciences Murdoch University Perth WA 6150, Australia
Paul Ressel
Affiliation:
Mathematisch-Geog raphische Fakultät Katholische Universität Eichstätt D-8078 Eichstätt Federal Republic of Germany
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Abstract

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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.

Keywords

60B0543A1043A35

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991, pp. 242 - 254
Copyright
Copyright © Canadian Mathematical Society 1991

References

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