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Título: Geronimus transformations of bivariate linear functionals
Impartida por: Misael Marriaga Castillo

Given a linear functional \(\mathbf{u}\) in the linear space of polynomials in two variables with real coefficients and a polynomial \(\lambda(x,y)\), in this contribution we deal with Geronimus transformations of \(\mathbf{u}\), i.e., those linear functionals \(\mathbf{v}\) such that \(\mathbf{u}=\lambda(x,y)\mathbf{v}\). The connection formulas between the sequences of bivariate orthogonal polynomials with respect to \(\mathbf{u}\) and \(\mathbf{v}\) are given. A matrix interpretation of such transformations by using \(LU\) and \(UL\) factorizations of the block Jacobi matrices associated with such polynomials is given. Finally, some illustrative examples of Geronimus transformations of weight functions supported in domains of \(\mathbb{R}^2\) are discussed.

This is a joint work with Francisco Marcellán (UC3M), Teresa E. Pérez (UGR), and Miguel Piñar (UGR).

29 de noviembre de 2019, 16:30, Seminario de la 1º planta del IEMath-GR