Tridiagonal operators and zeros of polynomials in two variables.(English)Zbl 1470.65092

Summary: 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.

MSC:

 65H04 Numerical computation of roots of polynomial equations 15B57 Hermitian, skew-Hermitian, and related matrices 33C47 Other special orthogonal polynomials and functions 42B37 Harmonic analysis and PDEs
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