论文信息 - Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres

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

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 jx1ja1 Ð Ð Ð jxdjad 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. Supported by the National Science Foundation under Grant DMS-9500532. Received by the editors February 6, 1995. AMS subject classification: 33C50, 33C45, 42C10.

Yuan Xu | Yuan Xu

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