Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
Classical Analysis and ODEs
2007-05-23 v1
Abstract
It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent polynomials on the unit circle. More precisely, it is a consequence of the five term recurrence relation obtained for these orthogonal Laurent polynomials, and the one to one correspondence established between them and the orthogonal polynomials on the unit circle. As an application, some results relating the behavior of the zeros of orthogonal polynomials and the location of Schur parameters are obtained.
Cite
@article{arxiv.math/0204300,
title = {Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle},
author = {Maria J. Cantero and Leandro Moral and Luis Velazquez},
journal= {arXiv preprint arXiv:math/0204300},
year = {2007}
}
Comments
25 pages