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
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