Publication: Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Análisis Aplicado | es |
dc.contributor.author | Beneteau, Catherine | |
dc.contributor.author | Condori, Alberto | |
dc.contributor.author | Liaw, Constanze | |
dc.contributor.author | Seco Forsnacke, Daniel | |
dc.contributor.author | Sola, Alan A. | |
dc.contributor.funder | Ministerio de Economía y Competitividad (España) | es |
dc.date.accessioned | 2021-06-07T10:52:59Z | |
dc.date.available | 2021-06-07T10:52:59Z | |
dc.date.issued | 2015-07 | |
dc.description.abstract | We study Dirichlet-type spaces Dα of analytic functions in the unit bidisk and their cyclic elements. These are the functions f for which there exists asequence(pn)∞n=1 of polynomials in two variables such that ‖pnf−1‖α→0 as n→∞. We obtain a number of conditions that imply cyclicity, and obtain sharp estimates on the best possible rate of decay of the norms ‖pnf−1‖α,in terms of the degree of pn, for certain classes of functions using results concerning Hilbert spaces of functions of one complex variable and comparisons between norms in one and two variables. We give examples of polynomials with no zeros on the bidisk that are not cyclic in Dα for α >1/2 (including the Dirichlet space); this is in contrast with the one-variable case where all nonvanishing polynomials are cyclic in Dirichlet-type spaces that are not algebras (α≤1). Further, we point out the necessity of a capacity zero condition on zero sets (in an appropriate sense) for cyclicity in the setting of the bidisk, and conclude by stating some open problems. | en |
dc.description.sponsorship | Liaw is partially supported by the NSF grant DMS-1261687. Seco is supported by ERC Grant 2011-ADG-20110209 from EU programme FP2007-2013, and by MEC/MICINN Project MTM2011-24606. Sola acknowledges support from the EPSRC under grant EP/103372X/1. | en |
dc.format.extent | 24 | |
dc.identifier.bibliographicCitation | First published in Pacific Journal of Mathematics in Vol. 276 (2015), No. 1, published by Mathematical Sciences Publishers | en |
dc.identifier.doi | https://doi.org/10.2140/pjm.2015.276.35 | |
dc.identifier.issn | 0030-8730 | |
dc.identifier.publicationfirstpage | 35 | |
dc.identifier.publicationissue | 1 | |
dc.identifier.publicationlastpage | 58 | |
dc.identifier.publicationtitle | Pacific Journal of Mathematics | en |
dc.identifier.publicationvolume | 276 | |
dc.identifier.uri | https://hdl.handle.net/10016/32841 | |
dc.identifier.uxxi | AR/0000026422 | |
dc.language.iso | eng | |
dc.publisher | Mathematical Sciences Publishers (MSP) | en |
dc.relation.projectID | Gobierno de España. MTM2011-24606 | es |
dc.rights | © 2015 Mathematical Sciences Publishers | en |
dc.rights.accessRights | open access | en |
dc.subject.eciencia | Matemáticas | es |
dc.subject.other | Cyclicity | en |
dc.subject.other | Dirichlet-type spaces | en |
dc.subject.other | Optimal approximation | en |
dc.subject.other | Norm restrictions | en |
dc.title | Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk | en |
dc.type | research article | * |
dc.type.hasVersion | VoR | * |
dspace.entity.type | Publication |
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