### On two models of orthogonal polynomials and their applications

*J. Arvesú, F. Marcellán*

#### Resumen

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 rthogonality 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.

**Key words:** Linear functionals, Orthogonal polynomials, Stieltjes and Markov functions, rational approximation, Hermite-Pad´e approximation, multiple orthogonal polynomials, trigonometric Moment problem, Quadratures on the unit circle, linear prediction, electrostatics of zeros.

**AMS subject classifications:** 33C45, 42C05

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