On the convergence of multi-level Hermite-Pad\'e approximants

TL;DR

This paper proves a convergence theorem for rational functions related to Hermite-Padé approximation of Nikishin systems and analyzes their asymptotic behavior, advancing understanding of multi-level approximation methods.

Contribution

It introduces a Stieltjes type convergence theorem for Hermite-Padé approximants of Nikishin systems and studies their ratio asymptotics, providing new theoretical insights.

Findings

Established convergence of Hermite-Padé approximants for Nikishin systems.

Analyzed the ratio asymptotic behavior of Hermite-Padé polynomials.

Extended classical results to a multi-level Hermite-Padé approximation context.

Abstract

In the present paper we prove a Stieltjes type theorem on the convergence of a sequence of rational functions associated with a mixed type Hermite-Pad\'e approximation problem of a Nikishin system of functions and analyze the ratio asymptotic of the corresponding Hermite-Pad\'e polynomials.