On a two variable class of Bernstein-Szego measures

TL;DR

This paper extends Bernstein-Szego theory from one variable to a specific class of two variable measures, constructing orthogonal polynomials and analyzing their recurrence coefficients.

Contribution

It introduces a two variable Bernstein-Szego measure class and develops orthogonal polynomials with their recurrence relations.

Findings

Orthogonal polynomials constructed for two variable measures

Recurrence coefficients analyzed for these polynomials

Extension of Bernstein-Szego theory to two variables

Abstract

The one variable Bernstein-Szego theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.