Uniform convergence of Hermite-Padé approximants for systems of Markov type functions
 
 
Description:  This talk deals with simultaneous rational approximation. In particular we study Hermite-Padé approximants of analytic and meromorphic functions of Markov type. The central results of this work is about of convergence of type I Hermite-Padé approximants of a Nikishin system. In the literature one can find a number of results on the convergence of type II Hermite-Padé approximants, but in this talk we present the first result about the convergence of type I Hermite-Padé approximants. Moreover, we study the convergence of type II Hermite-Padé approximants to a Nikishin system which has been perturbed by rational functions. This kind of problem was first study by A.A Gonchar in 1975 for the usual Padé approximantion. The generalization to Hermite-Padé for the case of m=2 (a system of two functions) was considered by Bustamante and Lagomasino in 1994. In this work the general case for any m is proved. Finally, we want to present some open problems related with this topic.
Date:  2014-10-24
Start Time:   14:30
Speaker:  Sergio Medina Peralta (Univ. Carlos III, Madrid, Spain)
Institution:  Univ. Carlos III of Madrid, Spain
Place:  Room 5.5
Research Groups: -Analysis
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