Rostyslav Kozhan: Multiple orthogonal polynomials on the unit circle and the Hermite-Pade approximation

Abstract:

We discuss properties of polynomials that are orthogonal simultaneously with respect to several measures on the unit circle. We define the analogues of Angelesco, AT, and Nikishin systems, for which the existence and uniqueness of multiple orthogonal polynomials hold at any location. This can be restated as the existence and uniqueness of the solution to a two-point Hermite-Pade approximation problem for Caratheodory functions.

The talk will also include a broad overview of the usual theory of orthogonal polynomials with respect to one or several measures on the real line and on the unit circle.