Three term relations formultivariate Uvarov orthogonal polynomials

Abstract

Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a givenmoment functional are studied. Existence of Uvarov orthogonal polynomials is analyzed, stating conditions to ensure it. The matrices of the three term relations of the Uvarov orthogonal polynomials are explicitly given in terms of the matrices of the three term relations satisfied by the original family. Two examples are presented in order to show that the results are valid for positive definite linear functionals and also for some quasi definite linear functionals which are not positive definite.