Convergence of row sequences of simultaneous Fourier-Pad\'e approximation

TL;DR

This paper proves a Montessus de Ballore type theorem for row sequences of simultaneous rational approximations based on Fourier expansions, advancing understanding of their convergence properties.

Contribution

It introduces a new convergence theorem for Fourier-based simultaneous rational approximations, extending classical results to this context.

Findings

Established convergence criteria for Fourier-based rational approximations

Proved a Montessus de Ballore type theorem for these approximations

Enhanced theoretical understanding of Fourier-Padé approximation convergence

Abstract

We consider row sequences of simultaneous rational approximations constructed in terms of Fourier expansions and prove a Montessus de Ballore type theorem.