Spherical basis functions and uniform distribution of points on spheres

Abstract

The main purpose of the present paper is to employ spherical basis functions (SBFs) to study uniform distribution of points on spheres. We extend Weyl's criterion for uniform distribution of points on spheres to include a characterization in terms of an SBF. We show that every set of minimal energy points associated with an SBF is uniformly distributed on the spheres. We give an error estimate for numerical integration based on the minimal energy points. We also estimate the separation of the minimal energy points.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/j.jat.2007.09.009

Keywords

uniform distribution of points, positive definite functions, Weyl's criterion, minimal energies, reproducing kernel Hilbert spaces, discrepancy

Publication Date

2008

Journal Title

Journal of Approximation Theory

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