# Seminario de Misael Marriaga Castillo

#### Detalles de Evento

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

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