Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants

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dc.contributor.author Bénéteau, Catherine
dc.contributor.author Khavinson, Dmitry
dc.contributor.author Sola, Alan A.
dc.contributor.author Liaw, Constanze
dc.contributor.author Seco Forsnacke, Daniel
dc.date.accessioned 2021-05-14T09:11:45Z
dc.date.available 2021-05-14T09:11:45Z
dc.date.issued 2016-12
dc.identifier.bibliographicCitation Bénéteau, 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.
dc.identifier.issn 0024-6107
dc.identifier.uri http://hdl.handle.net/10016/32632
dc.description.abstract We 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.
dc.description.sponsorship This 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.
dc.format.extent 21
dc.language.iso eng
dc.publisher Wiley
dc.rights © 2016 London Mathematical Society
dc.title Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1112/jlms/jdw057
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2014-51824-P
dc.relation.projectID Gobierno de España. MTM2011-24606
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 726
dc.identifier.publicationissue 3
dc.identifier.publicationlastpage 746
dc.identifier.publicationtitle Journal of the London Mathematical Society
dc.identifier.publicationvolume 94
dc.identifier.uxxi AR/0000026420
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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