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Negative definite and Schoenberg functions on commutative hypergroups

Part of: Abstract harmonic analysis Integral transforms, operational calculus

Published online by Cambridge University Press:  09 April 2009

Walter R. Bloom  and
Paul Ressel
Walter R. Bloom
Affiliation:
Division of Science and EngineeringMurdoch University Perth, WA 6150Australia e-mail: w.bloom@murdoch.edu.au
Paul Ressel
Affiliation:
Mathematisch-Geographische FakultätKatholische Universität Eichstätt85072 EichstättGermany e-mail: paul.ressel@ku-eichstaett.de
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Abstract

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In this paper we investigate when negative definite functions on commutative hypergroups satisfy the Schoenberg criterion.

Keywords

hypergrouppositive definitenegative definiteSturm-LiouvilleSchoenbergquadratic form

MSC classification

Secondary: 43A62: Hypergroups 43A10: Measure algebras on groups, semigroups, etc. 44A60: Moment problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 25 - 37
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Berg, C., Christensen, J. P. R. and Ressel, P., Harmonic analysis on semigroups. Theory of positive definite and related functions (Springer, New York, 1984).CrossRefGoogle Scholar
[2]Bloom, W. R. and Heyer, H., Harmonic analysis of probability measures on hypergroups (Walter de Gruyter, Berlin, 1995).CrossRefGoogle Scholar
[3]Lasser, R., ‘Orthogonal polynomials and hypergroups’, Rend. Mat. 3 (1983), 185–209.Google Scholar
[4]Voit, M., ‘Negative definite functions on commutative hypergroups’, in: Probability measures on groups, IX (Oberwolfach 1988), Lecture Notes in Math. 1379 (Springer, Berlin, 1989) pp. 376–388.CrossRefGoogle Scholar