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


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.


© 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:

ORCID [Knese]

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