Simultaneous Universal Pade-Taylor Approximation

TL;DR

This paper demonstrates that in various function spaces, Pade approximants and Taylor series can simultaneously approximate functions universally, with results applicable to multiple centers of expansion.

Contribution

It establishes the simultaneous universal approximation property of Pade and Taylor approximants, extending the phenomenon across different spaces and multiple centers.

Findings

Universal approximation holds for Pade and Taylor series in holomorphic function spaces.

Results apply to both single and multiple centers of expansion.

The phenomenon is generic in the considered function spaces.

Abstract

We prove simultaneous Universal Approximation of a certain type of Pade Approximants and of Taylor series with the same indexes. This is a generic phenomenon in the space of holomorphic functions in any simply connected domain, as well as in several other spaces. Our results are valid for one center of expansion and for several centers, as well.