LIE THEOREMS FOR ONE DIMENSIONAL HYPERGROUPS

Authors: GALLARDO*, L.¹; TRIME`CHE, K.²

Source: Integral Transforms and Special Functions, Volume 13, Number 1, 1 January 2002 , pp. 71-92(22)

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Abstract:

All known hypergroups on <$>[0, + infty[<$> are associated to second order differential operators on <$>]0, +infty[<$> of Sturm-Liouville type. It has been recognized as a crucial problem to determine if every hypergroup on <$>[0, +infty[<$> is of this type. In this paper we give an answer to this question. Moreover we show that a Laplace representation formula with non negative kernel always holds for the characters of the hypergroup.

Keywords: Sturm-Liouville hypergroups; Laplace representation formula

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10652460212890

Affiliations: 1: De´partement de Mathe´matiques, Universite´ de Tours Faculte´ des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France 2: Faculty of Sciences of Tunis, Department of Mathematics, Campus 1060 Tunis, Tunisia

Publication date: 2002-01-01

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