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 $\mathbf{f}$ 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.

19 pages. arXiv admin note: text overlap with arXiv:1502.03958