Simultaneous Universal Pad\'e Approximation

TL;DR

This paper establishes the existence of simultaneous universal Padé approximants for multiple types and centers, demonstrating their genericity in various function spaces including holomorphic functions and formal power series.

Contribution

It introduces new results on simultaneous universal Padé approximation applicable to multiple centers and types, expanding the scope of approximation theory.

Findings

Universal Padé approximants exist simultaneously for several types.

Results hold in spaces of holomorphic functions, formal power series, and subspaces of A^{}.

Applicability to multiple centers of expansion.

Abstract

We prove simultaneous universal Pad\'{e} approximation for several universal Pad\'{e} approximants of several types. Our results are generic in the space of holomorphic functions, in the space of formal power series as well as in a subspace of $A^{\infty}$. These results are valid for one center of expansion or for several centers as well.