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Δ-Sobolev orthogonal polynomials of Meixner type: asymptotics and limit relation

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorArea, Iván
dc.contributor.authorGodoy, Eduardo
dc.contributor.authorMarcellán Español, Francisco José
dc.contributor.authorMoreno Balcázar, Juan José
dc.date.accessioned2009-12-04T12:34:30Z
dc.date.available2009-12-04T12:34:30Z
dc.date.issued2005-06
dc.description16 pages, no figures.-- MSC2000 codes: 42C05.-- Issue title: "Proceedings of the Seventh International Symposium on Orthogonal Polynomials, Special Functions and Applications" (University of Copenhagen, Denmark, Aug 18-22, 2003).
dc.descriptionMR#: MR2127867 (2006a:33005)
dc.descriptionZbl#: Zbl 1060.42015
dc.description.abstractLet $\{Q_n(x)\}_n$ be the sequence of monic polynomials orthogonal with respect to the Sobolev-type inner product $$\bigl\langle (p(x),r(x)\bigr \rangle_S=\bigl\langle{\bold u}_0,p(x)r(x) \bigr\rangle+ \lambda\bigl\langle {\bold u}_1,(\Delta p)(x)(\Delta r)(x) \bigr\rangle,$$ where $\lambda\ge 0$, $(\Delta f)(x)=f(x+1)-f(x)$ denotes the forward difference operator and $({\bold u}_0,{\bold u}_1)$ is a $\Delta$-coherent pair of positive-definite linear functionals being ${\bold u}_1$ the Meixner linear functional. In this paper, relative asymptotics for the $\{Q_n(x)\}_n$ sequence with respect to Meixner polynomials on compact subsets of $\bbfC\setminus[0,+\infty)$ is obtained. This relative asymptotics is also given for the scaled polynomials. In both cases, we deduce the same asymptotics as we have for the self-$\Delta$-coherent pair, that is, when ${\bold u}_0={\bold u}_1$ is the Meixner linear functional. Furthermore, we establish a limit relation between these orthogonal polynomials and the Laguerre-Sobolev orthogonal polynomials which is analogous to the one existing between Meixner and Laguerre polynomials in the Askey scheme.
dc.description.sponsorshipThe work by I.A. and E.G. was partially supported by Ministerio de Ciencia y Tecnología of Spain under grant BFM2002-04314-C02-01. The work by F.M. has been supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM2003-06335-C03-02 as well as by the NATO collaborative grant PST.CLG. 979738. The work by J.J.M.B has been supported by Dirección General de Investigación of Spain under grant BFM2001-3878-C02-02 as well as by Junta de Andalucía (research group FQM0229).
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationJournal of Computational and Applied Mathematics, 2005, vol. 178, n. 1-2, p. 21-36
dc.identifier.doi10.1016/j.cam.2004.08.008
dc.identifier.issn0377-0427
dc.identifier.urihttps://hdl.handle.net/10016/5953
dc.language.isoeng
dc.publisherElsevier
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.cam.2004.08.008
dc.rights© Elsevier
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherOrthogonal polynomials
dc.subject.otherSobolev orthogonal polynomials
dc.subject.otherMeixner polynomials
dc.subject.otherΔ-coherent pairs
dc.subject.otherAsymptotics
dc.subject.otherLinear functionals
dc.titleΔ-Sobolev orthogonal polynomials of Meixner type: asymptotics and limit relation
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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