On two models of orthogonal polynomials and their applications

37 pages, no figures.-- MSC2000 codes: 33C45, 42C05.This contribution deals with some models of orthogonal polynomials as well as their applications in several areas of mathematics. Some new trends in the theory of orthogonal polynomials are summarized. In particular, we emphasize on two kinds of orthogonality, i.e., the standard orthogonality in the unit circle and a non standard one, which is called multi-orthogonality. Both have attracted the interest of researchers during the past ten years.This work has been supported by Dirección General de Investigación (MCyT) of Spain under grant BFM2000-0206-C04-01 and INTAS project 2000-272. J. Arvesú was partially supported by the Dirección General de Investigación (Comunidad Autónoma de Madrid).Publicad