arXiv subjects

Y. Zaldivar Gerpe

Publications and source records attributed to Y. Zaldivar Gerpe.

3 recordsLinked to original sources

arXiv2018

Direct and Inverse Results for Multipoint Hermite-Pade Approximants

Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of multipoint Hermite-Pade approximants. The exact rate of convergence of these denominators and of the approximants themselves is given in terms of the analytic properties of the system of functions. These results allow to detect the location of the poles of the system of functions which are in some sense closest to E.

math.CV↗

arXiv2018

Higher order recurrences and row sequences of Hermite-Padé approximation

We obtain extensions of the Poincaré and Perron theorems for higher order recurrence relations and apply them to obtain an inverse type theorem for row sequences of (type II) Hermite-Padé approximation of a vector of formal power series.

math.CV↗

arXiv2017

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 ${\bf f}$ 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 ${\bf f}$ and restate some conjectures corresponding to questions once posed by A. A. Gonchar for row sequences of Padé approximants.

math.CV↗