Rational approximation and Sobolev-type orthogonality

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dc.contributor.author Díaz González, Abel
dc.contributor.author Pijeira Cabrera, Héctor Esteban
dc.contributor.author Pérez Yzquierdo, Ignacio
dc.date.accessioned 2022-01-26T09:03:21Z
dc.date.issued 2020-12
dc.identifier.bibliographicCitation Díaz-González, A., Pijeira-Cabrera, H. & Pérez-Yzquierdo, I. (2020). Rational approximation and Sobolev-type orthogonality. Journal of Approximation Theory, 260, 105481.
dc.identifier.issn 0021-9045
dc.identifier.uri http://hdl.handle.net/10016/33961
dc.description.abstract In 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.
dc.description.sponsorship Abel 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.
dc.format.extent 19
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2020 Elsevier Inc. All rights reserved.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Rational approximation
dc.subject.other Sobolev orthogonality
dc.subject.other Markov's theorem
dc.subject.other Zero location
dc.title Rational approximation and Sobolev-type orthogonality
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.jat.2020.105481
dc.rights.accessRights embargoedAccess
dc.relation.projectID Gobierno de España. BES-2016-076613
dc.relation.projectID Gobierno de España. PGC2018-096504-B-C33
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 105481
dc.identifier.publicationlastpage 19
dc.identifier.publicationtitle Journal of Approximation Theory
dc.identifier.publicationvolume 260
dc.identifier.uxxi AR/0000027784
carlosiii.embargo.liftdate 2022-12-01
carlosiii.embargo.terms 2022-12-01
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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