Duality of Commutative Hypergroups

Hansmartin Zeuner
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Hansmartin Zeuner: Universität Tübingen, Mathematisches Institut

A chapter in Probability Measures on Groups X, 1991, pp 467-488 from Springer

Abstract: Abstract In this article the class of hypergroups having a dual hypergroup is examined. The heredity of this property under homomorphisms, orbital morphisms, products, joins and for subhypergroups is studied. It is shown that every Sturm-Liouville hypergroup on ℝ+ having a dual hypergroup is a Bessel-Kingman hypergroup and that every Sturm-Liouville hypergroup on a compact interval having a polynomial dual hypergroup is in the class of compact Jacobi hypergroups. Furthermore a new class of Sturm-Liouville hypergroups on the compact interval is introduced.

Keywords: Compact Group; Haar Measure; Jacobi Polynomial; Compact Interval; Compact Abelian Group (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2364-6_35

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DOI: 10.1007/978-1-4899-2364-6_35

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