Inverse results on row sequences of Hermite–Padé approximation

Abstract

We consider row sequences of (type II) Hermite–Padé approximations with common denominator associated with a vector f of formal power expansions about the origin. In terms of the asymptotic behavior of the sequence of common denominators, we describe some analytic properties of f and restate some conjectures corresponding to questions once posed by A. A. Gonchar for row sequences of Padé approximants.