Seminario de Francisco Marcellán

20 noviembre, 2018
12:00 pma1:00 pm

Speaker: Francisco Marcellán (Universidad Carlos III de Madrid).

Title: “A friendly approach to orthogonal polynomials and their applications”.

Date: martes 20 de noviembre, 12:00 horas.

Localication: Aula 0.2 del CIO (Edificio Torretamarit).

Abstract. The theory of orthogonal polynomials constitutes a nice example of the interplay between classical analysis, numerical analysis, linear algebra, probability theory and mathematical physics and update the classical monographs and constitute good approaches to those topics from different points of view. In this talk we will deal with orthogonal polynomials associated with measures supported on the real line with a special emphasis on the situations where they are eigenfunctions of higher order linear differential operators. Analytic properties of such polynomials in a more general framework will be discussed. Some applications in quadrature rules and boundary value problems will be analyzed. The link with integrable systems (Toda lattices) will be shown following. On the other hand, orthogonal polynomials with respect to nontrivial probability measures supported on the unit circle appear in the study of best linear predictors in filter theory. We will review some methods concerning the generation of such polynomials, their asymptotic behavior as well as the distribution of their zeros. Some applications to Szegő quadratures and integrable systems, in particular Schur flows, will be presented.