On the convergence of Hermite-Pade approximants for rational perturbations of a Nikishin system

Analysis Seminar
Wednesday, May 6, 2015 - 2:00pm
1 hour (actually 50 minutes)
Skiles 005
University of Madrid Carlos III
In the recent past multiple orthogonal polynomials have attracted great attention. They appear in simultaneous rational approximation, simultaneous quadrature rules, number theory, and more recently in the study of certain random matrix models. These are sequences of polynomials which share orthogonality conditions with respect to a system of measures. A central role in the development of this theory is played by the so called Nikishin systems of measures for which many results of the standard theory of orthogonal polynomials has been extended. In this regard, we present some results on the convergence of type I and type II Hermite-Pade approximation for a class of meromorphic functions obtained by adding vector rational functions with real coefficients to a Nikishin system of functions (the Cauchy transforms of a Nikishin system of measures).