English

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