Geodesic
Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 175-192

Voir la notice de l'article provenant de la source Cambridge University Press

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 |x 1|α 1 . . . |xd |αd on the unit sphere S d-1 in Rd . The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.
DOI : 10.4153/CJM-1997-009-4
Mots-clés : 33C50, 33C45, 42C10, Orthogonal polynomials in several variables, sphere, h-harmonics 
Xu, Yuan. Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres. Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 175-192. doi: 10.4153/CJM-1997-009-4
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