Discrepancy of minimal Riesz energy points

2019/07/10 by Marzo, Jordi, Mas, Albert · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.04814

Abstract

We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere \mathbb S^d. Our results are based in bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in \mathbb S² were obtained. Our result improves previously known bounds for 0≤ s<2 and s≠ 1 in \mathbb S², where s=0 is Wolff's result, and for d-t₀

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• An improved lower bound for the logarithmic energy on \mathbb S²

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