Continuous Hahn Polynomials of Differential Operator Argument and Analysis on Riemannian Symmetric Spaces of Constant Curvature

Badertscher, Erich ; Koornwinder, Tom H.

Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 750-773

Résumé

For the three types of simply connected Riemannian spaces of constant curvature it is shown that the associated spherical functions can be obtained from the corresponding (zonal) spherical functions by application of a differential operator of the form p(i d/dt), where p belongs to a system of orthogonal polynomials: Gegenbauer polynomials, Hahn polynomials or continuous symmetric Hahn polynomials. We give a group theoretic explanation of this phenomenon and relate the properties of the polynomials p to the properties of the corresponding representation. The method is extended to the case of intertwining functions.

Détail

DOI : 10.4153/CJM-1992-044-4

Mots-clés : 43A90, 43A85, 33C80, 33C45, spaces of constant curvature, spherical functions, associated spherical functions, Bessel functions, Jacobi functions, Gegenbauer polynomials, Hahn polynomials, continuous symmetric Hahn polynomials.

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