Inverse Results on Row Sequences of Hermite–Padé Approximation

We consider row sequences of (type II) Hermite–Padé approximations with common denominator associated with a vector $\mathbf f$ 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 $\mathbf f$ and restate some conjectures corresponding to questions once posed by A. A. Gonchar for row sequences of Padé approximants.