Orthogonal Laurent Polynomials of Two Real Variables

Abstract

In this paper we consider an appropriate ordering of the Laurent monomials xiyj , i,j∈Z that allows us to study sequences of orthogonal Laurent polynomials of the real variables x and y with respect to a positive Borel measure μdefined on R2 such that {x=0}∪{y=0}∉supp(μ) . This ordering is suitable for considering the {\em multiplication plus inverse multiplication operator} on each varibale (x+1x and y+1y) , and as a result we obtain five-term recurrence relations, Christoffel-Darboux and confluent formulas for the reproducing kernel and a related Favard's theorem. A connection with the one variable case is also presented, along with some applications for future research.