Universality at an Endpoint for Orthogonal Polynomials with Geronimus-Type Weights
Classical Analysis and ODEs
2021-08-11 v1
Abstract
We provide a new closed form expression for the Geronimus polynomials on the unit circle and use it to obtain new results and formulas. Among our results is a universality result at an endpoint of an arc for polynomials orthogonal with respect to a Geronimus type weight on an arc of the unit circle. The key tool is a formula of McLaughlin for powers of a two-by-two matrix, which we use to derive convenient formulas for Geronimus polynomials.
Keywords
Cite
@article{arxiv.1708.05781,
title = {Universality at an Endpoint for Orthogonal Polynomials with Geronimus-Type Weights},
author = {Brian Simanek},
journal= {arXiv preprint arXiv:1708.05781},
year = {2021}
}
Comments
13 pages