On separation of minimal Riesz energy points on spheres in Euclidean spaces

Authors:
A. B. J. Kuijlaars;E. B. Saff;X. Sun
Affiliations:
Department of Mathematics, Katholieke Universiteit Leuven, Leuven (Heverlee), Belgium;Center for Constructive Approximation, Department of Mathematies, Vanderbilt University, Nashville, TN;Department of Mathematics, Missouri State University, Springfield, MO
Venue:
Journal of Computational and Applied Mathematics - Special issue: Special functions in harmonic analysis and applications
Year:
2007

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Abstract

Let Sd denote the unit sphere in the Euclidean space Rd + 1 (d ≥ 1). Let N be a natural number (N≥ 2), and let ωN := {x1,...,xN} be a collection of N distinct points on Sd on which the minimal Riesz s-energy is attained. In this paper, we show that the points x1,...,xN are well-separated for the cases d - 1 ≤ s d.