Orthogonal Laurent polynomials of two real variables

2024/04/22 by Cruz-Barroso, Ruymán, Fernández, Lidia
#33C45 #42C05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2404.14303

Abstract

In this paper we consider an appropriate ordering of the Laurent monomials xⁱy^j, 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 μ defined on ℝ² such that \ x=0 \∪ \ y=0 \ \not∈ \textrmsupp(μ). This ordering is suitable for considering the \em multiplication plus inverse multiplication operator on each varibale ( x+(1)/(x). and . y+(1)/(y)), 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.

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