The Bergman Shift Operator on Polynomial Lemniscates
Classical Analysis and ODEs
2021-08-11 v2 Spectral Theory
Abstract
We investigate the relationship between the Bergman shift operator and the support of the corresponding measure. We pay special attention to the situation when the measure of orthogonality is concentrated on a polynomial lemniscate. As an application of our new results, we obtain a ratio asymptotic result for a wide variety of measures supported on polynomial lemniscates.
Cite
@article{arxiv.1307.1941,
title = {The Bergman Shift Operator on Polynomial Lemniscates},
author = {Brian Simanek},
journal= {arXiv preprint arXiv:1307.1941},
year = {2021}
}
Comments
15 pages; version 2: small correction to Lemma 4.1, extended bibliography