Conference abstracts

Session C7 - Special Functions and Orthogonal Polynomials

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Zeros of bivariate classical orthogonal polynomials on the unit disk

Teresa E. Perez

Universidad de Granada, Spain   -   tperez@ugr.es

The behaviour of the zeros of orthogonal polynomials in one variable has been studied extensively for years. In the positive-definite case, it is well know that the $n$th polynomial has exactly $n$ distinct zeros, that have important applications in quadrature formulae. In its classical sense, a zero of a bivariate orthogonal polynomial is an algebraic curve, and depends on the chosen basis in every case.

As far as we know, in two variables, the problem was tackled by Charles Hermite in 1865 for the biorthogonal basis of classical orthogonal polynomials on the unit disk. This work is devoted to show some old and new results, difficulties and open problems about this subject.

Joint work with Antonia M. Delgado (Universidad de Granada, Spain), Lidia Fernández (Universidad de Granada, Spain) and Miguel A. Piñar (Universidad de Granada, Spain).

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