Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
نویسنده
چکیده
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 jx1jã1 Ð Ð Ð jxdjãd 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.
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