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Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres

Published online by Cambridge University Press:  20 November 2018

Yuan Xu
Yuan Xu*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon USA, 97403-1222 e-mail: yuan@math.uoregon.edu
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Abstract

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Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions |x1|α1 . . . |xd|αd on the unit sphere Sd-1 in ℝd. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.

Keywords

33C5033C4542C10Orthogonal polynomials in several variablessphereh-harmonics
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 1 , 01 February 1997 , pp. 175 - 192
Copyright
Copyright © Canadian Mathematical Society 1997

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