2-Orthogonal Polynomials and Darboux Transforms

Abstract

In this work we present a new interpretation of Darboux transforms in the context of 2-orthogonal polynomials and nd condi- tions in order for any Darboux transform to yield a new set of 2- orthog- onal polynomials. We also introduce the LU and UL factorizations of the monic Jacobi matrix associated with a quasi-de nite linear functional de ned on the linear space of polynomials with real coe¢ cients.