The aim of this paper is to connect the zeros of polynomials in two variables with the eigenvalues of a self-adjoint operator. This is done by use of a functional-analytic method. The polynomials in two variables are assumed to satisfy a five-term recurrence relation, similar to the three-term recurrence relation that the classical orthogonal polynomials satisfy.
"Tridiagonal Operators and Zeros of Polynomials in Two Variables." Abstr. Appl. Anal. 2016 1 - 8, 2016. https://doi.org/10.1155/2016/6301413