English

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.

Keywords

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

R2 v1 2026-06-22T00:47:08.000Z