Orthogonal Laurent Polynomials of Two Real Variables Cruz Barroso, Ruymán Fernández Rodríguez, Lidia balanced ordering Christoffel–Darboux and confluent formula Favard’s theorem 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. 2024-11-20T10:38:50Z 2024-11-20T10:38:50Z 2024-10-26 journal article Cruz-Barroso, R. and Fernández, L. (2024), Orthogonal Laurent Polynomials of Two Real Variables. Stud Appl Math. e12783. https://doi.org/10.1111/sapm.12783 https://hdl.handle.net/10481/97136 10.1111/sapm.12783 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Wiley