Tridiagonal Operators and Zeros of Polynomials in Two Variables

الملخص EN

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.