Three term relations for multivariate Uvarov orthogonal polynomials

Three term relations for orthogonal polynomials in several variables associated to a moment linear functional obtained by a Uvarov modification of a given moment 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.

Automated summary

This paper studies the three term relations of orthogonal polynomials in several variables associated with a moment linear functional obtained by a Uvarov modification. It analyzes the existence of Uvarov orthogonal polynomials and provides conditions to ensure their existence. The matrices of the three term relations for the Uvarov orthogonal polynomials are explicitly given based on the matrices of the three term relations satisfied by the original family. Two examples are presented to demonstrate the validity of the results for positive definite linear functionals and some quasi definite linear functionals which are not positive definite.