Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems

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Show simple item record Bénéteau, Catherine Khavinson, Dmitry S. Liaw, Constanze Seco Forsnacke, Daniel Simanek, Brian 2021-05-20T09:13:01Z 2021-05-20T09:13:01Z 2019-02-19
dc.identifier.bibliographicCitation Revista matemática iberoamericana, 35(2), Feb. 2019, Pp. 607-642
dc.identifier.issn 0213-2230
dc.identifier.issn 2235-0616 (online)
dc.description.abstract We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we find the minimum possible modulus of occurring zeros via a nonlinear extremal problem associated with norms of Jacobi matrices. We examine global properties of these zeros and prove Jentzsch-type theorems describing where they accumulate. As a consequence, we obtain detailed information regarding zeros of reproducing kernels in weighted spaces of analytic functions.
dc.description.sponsorship The authors would like to thank A. Sola for useful discussions, and the National Science Foundation for their support of the SEAM conference in 2016, where some of this work was carried out. Beneteau and Khavinson are grateful to the Centre de Recherches Mathematiques in Montreal for hosting them during the spring semester of 2016. Khavinson acknowledges the support of grant #513381 from the Simons Foundation. Liaw's work is supported by the National Science Foundation DMS-1802682. Seco acknowledges support from Ministerio de Economía y Competitividad Project MTM2014-51824-P and from Generalitat de Catalunya Project 2014SGR289.
dc.format.extent 36
dc.language.iso eng
dc.publisher European Mathematical Society
dc.rights © European Mathematical Society
dc.subject.other Bergman spaces
dc.subject.other Dirichlet spaces
dc.subject.other Cyclic functions
dc.subject.other Orthogonal polynomials
dc.title Zeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theorems
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2014-51824-P
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 607
dc.identifier.publicationissue 2
dc.identifier.publicationlastpage 642
dc.identifier.publicationtitle REVISTA MATEMATICA IBEROAMERICANA
dc.identifier.publicationvolume 35
dc.identifier.uxxi AR/0000023670
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Análisis Aplicado
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