On the convergence of type I Hermite-Padé approximants

Abstract

Padé approximation has two natural extensions to vector rational approximation through the so called type I and type II Hermite-Padé approximants. The convergence properties of type II Hermite-Padé approximants have been studied. For such approximants Markov and Stieltjes type theorems are available. To the present, such results have not been obtained for type I approximants. In this paper, we provide Markov and Stieltjes type theorems on the convergence of type I Hermite-Padé approximants for Nikishin systems of functions.

arXiv comment20 pages