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Generalized hypergroups and orthogonal polynomials

Published online by Cambridge University Press:  22 January 2016

Nobuaki Obata  and
Norman J. Wildberger
Nobuaki Obata
Affiliation:
Graduate School of Polymathematics, Nagoya University, Nagoya, 464-01, Japan
Norman J. Wildberger
Affiliation:
School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
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We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthogonal polynomials, and many results of harmonic analysis on locally compact abelian groups can be carried over to the case of commutative hypergroups; see Heyer [11], Litvinov [17], Ross [22], and references cited therein. Orthogonal polynomials have been studied in terms of hypergroups by Lasser [15] and Voit [31], see also the works of Connett and Schwartz [6] and Schwartz [23] where a similar spirit is observed.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 142 , June 1996 , pp. 67 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

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