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

Simple item page
dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorBénéteau, Catherine
dc.contributor.authorKhavinson, Dmitry S.
dc.contributor.authorLiaw, Constanze
dc.contributor.authorSeco Forsnacke, Daniel
dc.contributor.authorSimanek, Brian
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-05-20T09:13:01Z
dc.date.available2021-05-20T09:13:01Z
dc.date.issued2019-02-19
dc.description.abstractWe 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.en
dc.description.sponsorshipThe 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.en
dc.format.extent36es
dc.identifier.bibliographicCitationRevista matemática iberoamericana, 35(2), Feb. 2019, Pp. 607-642es
dc.identifier.doihttps://doi.org/10.4171/RMI/1064
dc.identifier.issn0213-2230
dc.identifier.issn2235-0616 (online)
dc.identifier.publicationfirstpage607es
dc.identifier.publicationissue2es
dc.identifier.publicationlastpage642es
dc.identifier.publicationtitleREVISTA MATEMATICA IBEROAMERICANAes
dc.identifier.publicationvolume35es
dc.identifier.urihttps://hdl.handle.net/10016/32695
dc.identifier.uxxiAR/0000023670
dc.language.isoengen
dc.publisherEuropean Mathematical Societyen
dc.relation.projectIDGobierno de España. MTM2014-51824-Pes
dc.rights© European Mathematical Societyen
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherBergman spacesen
dc.subject.otherDirichlet spacesen
dc.subject.otherCyclic functionsen
dc.subject.otherOrthogonal polynomialsen
dc.titleZeros of optimal polynomial approximants: Jacobi matrices and Jentzsch-type theoremsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
zeros_RMI_2019_ps.pdf
Size:
576.27 KB
Format:
Adobe Portable Document Format
Download
Collections
DM - GAMA - Artículos de Revistas
Proyectos FOS (2022-2023)