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Abstract and Applied Analysis
Volume 2016 (2016), Article ID 6301413, 8 pages
Research Article

Tridiagonal Operators and Zeros of Polynomials in Two Variables

1Department of Mathematics, University of Patras, 26500 Patras, Greece
2Department of Civil Engineering, University of Patras, 26500 Patras, Greece

Received 7 December 2015; Revised 16 February 2016; Accepted 18 February 2016

Academic Editor: Lucas Jódar

Copyright © 2016 Chrysi G. Kokologiannaki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.