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.References
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Additional Information
- Catherine Bénéteau
- Affiliation: Department of Mathematics, University of South Florida, 4202 E. Fowler Avenue, Tampa, Florida 33620-5700
- Email: cbenetea@usf.edu
- Greg Knese
- Affiliation: Department of Mathematics, Washington University in St. Louis, One Brookings Drive, Campus Box 1146, St. Louis, Missouri 63130-4899
- MR Author ID: 813491
- Email: geknese@math.wustl.edu
- Łukasz Kosiński
- Affiliation: Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland – and – Département de mathématiques et de statistique, Pavillon AlexandreVachon, 1045 av. de la Médecine, Université Laval, Québec (Québec) G1V 0A6, Canada
- MR Author ID: 825007
- Email: lukasz.kosinski@gazeta.pl
- Constanze Liaw
- Affiliation: Department of Mathematics and CASPER, Baylor University, One Bear Place #97328, Waco, Texas 76798-7328
- MR Author ID: 877090
- Email: Constanze_Liaw@baylor.edu
- Daniel Seco
- Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
- Address at time of publication: Departament de Matemàtica Aplicada i Analisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
- Email: dseco@mat.uab.cat
- Alan Sola
- Affiliation: Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
- Address at time of publication: Department of Mathematics, University of South Florida, 4202 E. Fowler Avenue, Tampa, Florida 33620-5700
- MR Author ID: 804661
- Email: a.sola@statslab.cam.ac.uk
- Received by editor(s): November 4, 2014
- Published electronically: February 12, 2016
- Additional Notes: 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 - © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 8737-8754
- MSC (2010): Primary 32A37, 47A13; Secondary 14M99
- DOI: https://doi.org/10.1090/tran6689
- MathSciNet review: 3551587