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The purpose of this paper is to establish L^p error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere.
Positive definite functions on spheres
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Asymptotics and special functions
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Orthogonal Polynomials
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The best approximation of classes of functions W p α ( s n ) {W}^{\alpha}_{p}\,(s^{n}) by polynomials in spherical harmonics
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Constructive Approximation on the Sphere
Freeden, W., Gervens, T., and Schreiner, M · 1998
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