Cyclic polynomials in two variables

Catherine Bénéteau; Greg Knese; Lukasz KosiŃski; Constanze Liaw; Daniel Seco; Alan Sola

doi:10.1090/tran6689

Cyclic polynomials in two variables

Catherine Bénéteau, Greg Knese, Lukasz KosiŃski, Constanze Liaw, Daniel Seco, Alan Sola

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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.

Original language	English
Pages (from-to)	8737-8754
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	368
Issue number	12
DOIs	https://doi.org/10.1090/tran6689
State	Published - 2016

Keywords

Bidisk
Cyclicity
Determinantal representations
Dirichlet-type spaces

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10.1090/tran6689

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title = "Cyclic polynomials in two variables",

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.",

keywords = "Bidisk, Cyclicity, Determinantal representations, Dirichlet-type spaces",

author = "Catherine B{\'e}n{\'e}teau and Greg Knese and Lukasz Kosi{\'N}ski and Constanze Liaw and Daniel Seco and Alan Sola",

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year = "2016",

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T1 - Cyclic polynomials in two variables

AU - Bénéteau, Catherine

AU - Knese, Greg

AU - KosiŃski, Lukasz

AU - Liaw, Constanze

AU - Seco, Daniel

AU - Sola, Alan

PY - 2016

Y1 - 2016

N2 - 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.

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.

KW - Bidisk

KW - Cyclicity

KW - Determinantal representations

KW - Dirichlet-type spaces

UR - https://www.scopus.com/pages/publications/84990876787

U2 - 10.1090/tran6689

DO - 10.1090/tran6689

M3 - Article

AN - SCOPUS:84990876787

SN - 0002-9947

VL - 368

SP - 8737

EP - 8754

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 12

ER -

Cyclic polynomials in two variables

Abstract

Keywords

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