A semiclassical perspective on multivariate orthogonal polynomials

M. Alvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar

Published 2006-10-04Version 1

Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these polynomials including the analogous of the semiclassical Pearson differential equation, the structure relation and a differential--difference equation.