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On asymptotic properties of Freud–Sobolev orthogonal polynomials

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorCachafeiro, Alicia
dc.contributor.authorMarcellán Español, Francisco José
dc.contributor.authorMoreno Balcázar, Juan José
dc.date.accessioned2009-12-07T13:16:18Z
dc.date.available2009-12-07T13:16:18Z
dc.date.issued2003-11
dc.description16 pages, no figures.-- MSC2000 codes: 33C45; 33C47; 42C05.
dc.descriptionMR#: MR2016838 (2005e:33004)
dc.descriptionZbl#: Zbl 1043.33005
dc.description.abstractIn this paper we consider a Sobolev inner product $(f,g)_S=\int fg\,d\mu+ \lambda \int f'g'\,d\mu (*)$, and we characterize the measures μ for which there exists an algebraic relation between the polynomials, {Pn}, orthogonal with respect to the measure μ and the polynomials, {Qn}, orthogonal with respect to (*), such that the number of involved terms does not depend on the degree of the polynomials. Thus, we reach in a natural way the measures associated with a Freud weight. In particular, we study the case $d\mu=e^{-x^4}dx$ supported on the full real axis and we analyze the connection between the so-called Nevai polynomials (associated with the Freud weight $e^{-x^4}$)and the Sobolev orthogonal polynomials Qn. Finally, we obtain some asymptotics for {Qn}.
dc.description.sponsorshipResearch by first author (A.C.) partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under Grant BFM 2000 0015. Research by second author (F.M.) partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under Grant BFM2003 06335 C03 02, by INTAS Project 2000 272 and by the NATO collaborative Grant PST.CLG. 979738. Research by third author (J.J.M.-B.) partially supported by Junta de Andalucía, Grupo de Investigación FQM 0229, Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under Grant BFM 2001 3878 C02 02 and INTAS Project 2000 272.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Approximation Theory, 2004, vol. 125, n. 1, p. 26-41
dc.identifier.doi10.1016/j.jat.2003.09.003
dc.identifier.issn0021-9045
dc.identifier.urihttps://hdl.handle.net/10016/5977
dc.language.isoeng
dc.publisherElsevier
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.jat.2003.09.003
dc.rights© Elsevier
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherSobolev orthogonal polynomials
dc.subject.otherFreud polynomials
dc.subject.otherAsymptotics
dc.titleOn asymptotic properties of Freud–Sobolev orthogonal polynomials
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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