Convergence Speed for Fekete Points on Uniformly Polynomially Cuspidal Sets

TL;DR

This paper analyzes the convergence speed of Fekete points on specific polynomially cuspidal sets, establishing their regularity properties to derive convergence results.

Contribution

It introduces a method to determine convergence speed for Fekete points on polynomially cuspidal sets by proving their regularity in a specific sense.

Findings

Fekete points converge at a quantifiable speed on these sets.

The sets are shown to be $( ext{C}^ ext{alpha}, ext{C}^ ext{alpha'})$-regular.

Regularity properties facilitate convergence analysis.

Abstract

We obtain the convergence speed for Fekete points on uniformly polynomially cuspidal compact sets introduced by Pawlucki and Ple\'sniak. This is done by showing that these sets are $(\mathscr{C}^{\alpha}, \mathscr{C}^{\alpha'})$-regular in the sense of Dinh, Ma and Nguyen.