Cyclic polynomials in two variables

Bénéteau, Catherine; Knese, Greg; Kosiński, Łukasz; Liaw, Constanze; Seco, Daniel; Sola, Alan

doi:10.1090/tran6689

Cyclic polynomials in two variables
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by Catherine Bénéteau, Greg Knese, Łukasz Kosiński, Constanze Liaw, Daniel Seco and Alan Sola PDF

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

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.

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