Cyclic polynomials in two variables

Authors

Catherine Bénéteau
Greg Knese, Washington University in St. LouisFollow
Łukasz Kosiński
Constanze Liaw
Daniel Seco
Alan Sola

Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

2-12-2016

Originally Published In

Trans. Amer. Math. Soc. 368 (2016), 8737-8754

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 polynomials, and harmonic analysis on curves.

Comments

© Copyright 2016 American Mathematical Society Accepted manuscript version of article which was first published in Transactions of the American Mathematical Society in volume 368 (2016), pp. 8737-8754, published by the American Mathematical Society DOI: http://dx.doi.org/10.1090/tran6689

ORCID

http://orcid.org/0000-0002-9484-2537 [Knese]

Recommended Citation

Bénéteau, Catherine; Knese, Greg; Kosiński, Łukasz; Liaw, Constanze; Seco, Daniel; and Sola, Alan, "Cyclic polynomials in two variables" (2016). Mathematics Faculty Publications. 37.
https://openscholarship.wustl.edu/math_facpubs/37