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Cyclic polynomials in two variables

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URI: https://hdl.handle.net/10016/32634
ISSN: 0002-9947
DOI: https://doi.org/10.1090/tran6689
UXXI: AR/0000026421
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Cyclic_TAMS_2018_ps.pdf (671.33 KB)
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2016-12
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American Mathematical Society (AMS)
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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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Cyclicity, Dirichlet-type spaces, Bidisk, Determinantal representations
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Bénéteau, C., Knese, G., Kosiński, U., Liaw, C., Seco, D. & Sola, A. (2016). Cyclic polynomials in two variables. Transactions of the American Mathematical Society, 368(12), pp. 8737–8754.
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