Overconvergence of Some Simultaneous Hermite-Pade Interpolants

摘要

In a previous paper the authors gave an upper bound on the limsup of the n-throot of the difference between two rational Hermite-Pade interpolants to a d-tuple of meromorphic functions with a given fixed number of poles (disjoint pole sets for different functions). This paper addresses the problem of the number of points for which the upper bound is not achieved; the cases absolute z less than p and absolute z greater than p, where p is the radius of convergence for the functions with their poles removed, have to be distinguished. (Copyright (c) 1995 by Faculty of Technical Mathematics and Informatics, Delft.)