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Rational approximation and Sobolev-type orthogonality

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorDíaz González, Abel
dc.contributor.authorPijeira Cabrera, Héctor Esteban
dc.contributor.authorPérez Yzquierdo, Ignacio
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2022-01-26T09:03:21Z
dc.date.available2022-12-01T00:00:05Z
dc.date.issued2020-12
dc.description.abstractIn this paper, we study the sequence of orthogonal polynomials {Sn}∞ n=0 with respect to the Sobolev-type inner product ⟨ f, g⟩ = ∫ 1 −1 f (x)g(x) dµ(x) + ∑ N j=1 η j f (d j) (c j )g (d j) (c j ) where µ is a finite positive Borel measure whose support supp (µ) ⊂ [−1, 1] contains an infinite set of points, η j > 0, N, d j ∈ Z+ and {c1, . . . , cN } ⊂ R \ [−1, 1]. Under some restriction of order in the discrete part of ⟨·, ·⟩, we prove that for sufficiently large n the zeros of Sn are real, simple, n − N of them lie on (−1, 1) and each of the mass points c j “attracts” one of the remaining N zeros. The sequences of associated polynomials {S [k] n }∞ n=0 are defined for each k ∈ Z+. If µ is in the Nevai class M(0, 1), we prove an analogue of Markov’s Theorem on rational approximation to Markov type functions and prove that convergence takes place with geometric speed.en
dc.description.sponsorshipAbel Díaz González supported by the Research Fellowship Program, Ministry of Economy and Competitiveness of Spain under grant BES-2016-076613. Héctor Pijeira Cabrera research partially supported by Spanish State Research Agency, under grant PGC2018-096504-B-C33. Ignacio Pérez-Yzquierdo research partially supported by National Fund for Innovation and Scientific and Technological Development (FONDOCyT), Dominican Republic, under grant 2015-1D2-164.en
dc.format.extent19
dc.identifier.bibliographicCitationDíaz-González, A., Pijeira-Cabrera, H. & Pérez-Yzquierdo, I. (2020). Rational approximation and Sobolev-type orthogonality. Journal of Approximation Theory, 260, 105481.en
dc.identifier.doihttps://doi.org/10.1016/j.jat.2020.105481
dc.identifier.issn0021-9045
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue105481
dc.identifier.publicationlastpage19
dc.identifier.publicationtitleJournal of Approximation Theoryen
dc.identifier.publicationvolume260
dc.identifier.urihttp://hdl.handle.net/10016/33961
dc.identifier.uxxiAR/0000027784
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. BES-2016-076613es
dc.relation.projectIDGobierno de España. PGC2018-096504-B-C33es
dc.rights© 2020 Elsevier Inc. All rights reserved.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherRational approximationen
dc.subject.otherSobolev orthogonalityen
dc.subject.otherMarkov's theoremen
dc.subject.otherZero locationen
dc.titleRational approximation and Sobolev-type orthogonalityen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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