CMV matrices and little and big -1 Jacobi polynomials
Classical Analysis and ODEs
2011-08-23 v2 Mathematical Physics
math.MP
Abstract
We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related with the theory of CMV matrices. It contains an arbitrary parameter which leads to a linear operator pencil. We show that the little and big -1 Jacobi polynomials are naturally obtained under this map from the Jacobi polynomials on the unit circle.
Cite
@article{arxiv.1108.3535,
title = {CMV matrices and little and big -1 Jacobi polynomials},
author = {Maxim Derevyagin and Luc Vinet and Alexei Zhedanov},
journal= {arXiv preprint arXiv:1108.3535},
year = {2011}
}
Comments
20 pages; some typos are corrected