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Kokologiannaki, Chrysi G.; Petropoulou, Eugenia N.; Rizos, Dimitris

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

Abstr. Appl. Anal. 2016, Article ID 6301413, 8 p. (2016).
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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\textit{C. G. Kokologiannaki} et al., Abstr. Appl. Anal. 2016, Article ID 6301413, 8 p. (2016; Zbl 1470.65092)
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