English

Cyclic polynomials in two variables

Functional Analysis 2016-10-10 v1 Complex Variables

Abstract

We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the bidisk. The cyclicity of a polynomial depends on both the size and nature of the zero set of the polynomial on the distinguished boundary. The techniques in the proof come from real analytic function theory, determinantal representations for stable polynomials, and harmonic analysis on curves

Keywords

Cite

@article{arxiv.1408.3616,
  title  = {Cyclic polynomials in two variables},
  author = {Catherine Bénéteau and Greg Knese and Łukasz Kosiński and Constanze Liaw and Daniel Seco and Alan Sola},
  journal= {arXiv preprint arXiv:1408.3616},
  year   = {2016}
}

Comments

20 pages

R2 v1 2026-06-22T05:30:21.758Z