Analysis and Probability seminar

Abstract: We discuss properties of polynomials that are orthogonal with respect to several measures on the unit circle simultaneously. We show that for systems of Angelesco, AT, and Nikishin type, such polynomials always exist and are uniquely determined, just like for multiple orthogonality on the real line. 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 measure on the real line and on the unit circle, as well as multiple orthogonal polynomials on the real line.