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Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorBénéteau, Catherine
dc.contributor.authorKhavinson, Dmitry
dc.contributor.authorSola, Alan A.
dc.contributor.authorLiaw, Constanze
dc.contributor.authorSeco Forsnacke, Daniel
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-05-14T09:11:45Z
dc.date.available2021-05-14T09:11:45Z
dc.date.issued2016-12
dc.description.abstractWe study connections between orthogonal polynomials, reproducing kernel functions, and polynomials P minimizing Dirichlet‐type norms ∥pf−1∥α for a given function f . For α ∈ [0,1] (which includes the Hardy and Dirichlet spaces of the disk) and general f , we show that such extremal polynomials are non‐vanishing in the closed unit disk. For negative α , the weighted Bergman space case, the extremal polynomials are non‐vanishing on a disk of strictly smaller radius, and zeros can move inside the unit disk. We also explain how dist Dα (1, f · Pn) , where Pn is the space of polynomials of degree at most n , can be expressed in terms of quantities associated with orthogonal polynomials and kernels, and we discuss methods for computing the quantities in question.en
dc.description.sponsorshipThis work was supported by NSF under the grant DMS1500675. DS was supported by ERC Grant 2011-ADG-20110209 from EU programme FP2007-2013 and MEC Projects MTM2014-51824-P and MTM2011-24606.en
dc.format.extent21
dc.identifier.bibliographicCitationBénéteau, C., Khavinson, D., Sola, A. A., Liaw, C. & Seco, D. (2016). Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants. Journal of the London Mathematical Society, 94(3), pp. 726–746.en
dc.identifier.doihttps://doi.org/10.1112/jlms/jdw057
dc.identifier.issn0024-6107
dc.identifier.publicationfirstpage726
dc.identifier.publicationissue3
dc.identifier.publicationlastpage746
dc.identifier.publicationtitleJournal of the London Mathematical Societyen
dc.identifier.publicationvolume94
dc.identifier.urihttps://hdl.handle.net/10016/32632
dc.identifier.uxxiAR/0000026420
dc.language.isoeng
dc.publisherWiley
dc.relation.projectIDGobierno de España. MTM2014-51824-Pes
dc.relation.projectIDGobierno de España. MTM2011-24606es
dc.rights© 2016 London Mathematical Societyen
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.titleOrthogonal polynomials, reproducing kernels, and zeros of optimal approximantsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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