Mirror symmetric polynomials orthogonal on the unit circle
Classical Analysis and ODEs
2025-10-14 v1 Mathematical Physics
math.MP
Abstract
We introduce and study a special family of polynomials orthogonal on the unit circle (OPUC). These OPUC satisfy a mirror symmetry property of their Verblunsky coefficients. Several equivalent conditions for the OPUC to be mirror symmetric are presented. Corresponding unitary CMV matrices satisfy simple algebraic relations similar to relations for persymmetric tridiagonal matrices. We present three explicit examples of mirror symmetric OPUC.
Keywords
Cite
@article{arxiv.2510.10447,
title = {Mirror symmetric polynomials orthogonal on the unit circle},
author = {Alexei Zhedanov},
journal= {arXiv preprint arXiv:2510.10447},
year = {2025}
}
Comments
20 pages, 16 references