Funk - Hecke Formulae on Spheres and on Balls
نویسندگان
چکیده
منابع مشابه
Cubature formulae for spheres, simplices and balls
We obtain in explicit form the unique Gaussian cubature for balls (spheres) in Rn based on integrals over balls (spheres), centered at the origin, that integrates exactly all m-harmonic functions. In particular, this formula is exact for all polynomials in n variables of degree 2m − 1. A Gaussian cubature for simplices is also constructed. Upper bounds for the errors for certain smoothness clas...
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Orthogonal polynomials on the unit sphere in Rd+1 and on the unit ball in Rd are shown to be closely related to each other for symmetric weight functions. Furthermore, it is shown that a large class of cubature formulae on the unit sphere can be derived from those on the unit ball and vice versa. The results provide a new approach to study orthogonal polynomials and cubature formulae on spheres.
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Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T d. These formulae are used to derive cubature formulae on the surface of the sphere Sd and on the unit ball Bd using connections between cubature for...
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Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T . These formulae are used to derive cubature formulae on the surface of the sphere S and on the unit ball B using connections between cubature formul...
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