RT Journal Article
T1 Cyclic polynomials in two variables
A1 Bénéteau, Catherine
A1 Knese, Greg
A1 Kosinski, Lukasz
A1 Liaw, Constanze
A1 Seco Forsnacke, Daniel
A1 Sola, Alan A.
AB 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.
PB American Mathematical Society (AMS)
SN 0002-9947
YR 2016
FD 2016-12
LK https://hdl.handle.net/10016/32634
UL https://hdl.handle.net/10016/32634
LA eng
NO The second author was supported by NSF grant DMS-1363239.The third author was supported by NCN grant 2011/03/B/ST1/04758.The fourth author was partially supported by NSF grant DMS-1261687.The fifth author was supported by ERC Grant 2011-ADG-20110209 from EU programme FP2007-2013 and MEC/MICINN Project MTM2011-24606.The sixth author acknowledges support from the EPSRC under grant EP/103372X/1.
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RD 1 sept. 2024