Equidistribution of the Fekete points on the sphere

TL;DR

This paper proves that Fekete points on the sphere become uniformly distributed as their number increases, by linking them to other well-studied point arrays.

Contribution

It establishes the asymptotic equidistribution of Fekete points on the sphere through their connection with Marcinkiewicz-Zygmund and interpolating arrays.

Findings

Fekete points are asymptotically equidistributed on the sphere.

The proof uses their relation to other known point arrays.

Results support their suitability for interpolation and numerical integration.

Abstract

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently.