English

Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces

Complex Variables 2024-03-08 v1 Functional Analysis

Abstract

In this paper, we study the cyclic vectors of the shift operator SbS_b acting on de Branges-Rovnyak space H(b)\mathcal H(b) associated to a non-extreme point of the closed unit ball of HH^\infty. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity.

Keywords

Cite

@article{arxiv.2403.04335,
  title  = {Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces},
  author = {Emmanuel Fricain and Romain Lebreton},
  journal= {arXiv preprint arXiv:2403.04335},
  year   = {2024}
}