Universal Pad\'e Approximation

TL;DR

This paper extends the concept of universality from Taylor series to Padé approximants, achieving broader approximation capabilities on complex planar domains of arbitrary connectivity.

Contribution

It generalizes universal approximation results to Padé approximants, covering compact sets and planar domains of any connectivity, beyond simply connected regions.

Findings

Universal approximation on compact sets of arbitrary connectivity

Results applicable to planar domains of any connectivity

Stronger approximation properties than previous Taylor series results

Abstract

In transferring some results from universal Taylor series to the case of Pad\'e approximants we obtain stronger results, such as, universal approximation on compact sets of arbitrary connectivity and generic results on planar domains of any connectivity and not just on simply onnected domains.