Convergence of row sequences of simultaneous Pad\'{e}-Faber approximants

TL;DR

This paper proves a Montessus de Ballore type theorem for row sequences of vector-valued Padé-Faber approximants, advancing the understanding of their convergence properties.

Contribution

It establishes a convergence theorem for simultaneous Padé-Faber approximants, extending classical results to vector-valued cases.

Findings

Proves a Montessus de Ballore type theorem for these approximants.

Demonstrates convergence behavior of vector-valued Padé-Faber approximants.

Provides theoretical foundation for their use in approximation theory.

Abstract

We consider row sequences of vector valued Pad\'{e}-Faber approximants (simultaneous Pad\'{e}-Faber approximants) and prove a Montessus de Ballore type theorem.