Fourier-Pad\'e approximants for Angelesco systems

TL;DR

This paper investigates Fourier-Padé approximation methods for Angelesco systems, utilizing orthogonal polynomial expansions instead of power series, and compares linear and non-linear approaches similar to Hermite-Padé approximation.

Contribution

It introduces a Fourier-Padé approximation framework for Angelesco systems based on orthogonal polynomial expansions, extending Hermite-Padé techniques.

Findings

Develops a new approximation method for Angelesco systems

Analyzes properties of linear and non-linear Fourier-Padé approximants

Provides insights into convergence and accuracy of the approach

Abstract

In this paper we study linear and non-linear Fourier-Pad\'e approximation for Angelesco systems of functions. This construction is similar to that of Hermite-Pad\'e approximation. Instead of considering power series expansions of the functions in the system, we take their expansion in a series of orthogonal polynomials.