Asymptotics of Pad\'e approximants to a certain class of elliptic-type functions

TL;DR

This paper studies the uniform convergence behavior of Padé approximants for a class of elliptic functions represented as Cauchy integrals with Dini-continuous densities on specific continua, advancing understanding of approximation theory.

Contribution

It provides new results on the uniform convergence of Padé approximants for elliptic functions defined via Cauchy integrals on Chebotarëv continua, a class not extensively analyzed before.

Findings

Established conditions for uniform convergence of Padé approximants.

Extended approximation theory to elliptic functions with Dini-continuous densities.

Analyzed convergence on complex continua with specific geometric properties.

Abstract

In this paper we investigate the question of uniform convergence of Pad\'e approximants to elliptic functions that can be represented as Cauchy integrals of Dini-continuous non-vanishing densities given on 3-point Chebotar\"ev continua.