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Asymptotics for Sobolev orthogonal polynomials for exponential weights

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorGeronimo, Jeffrey S.
dc.contributor.authorLubinsky, D. S.
dc.contributor.authorMarcellán Español, Francisco José
dc.date.accessioned2009-12-04T11:00:07Z
dc.date.available2009-12-04T11:00:07Z
dc.date.issued2005-08
dc.description38 pages, no figures.-- MSC2000 codes: 42C05, 33C25.
dc.descriptionMR#: MR2164139 (2006c:41040)
dc.descriptionZbl#: Zbl 1105.42016
dc.description.abstract^aLet $\lambda >0,\alpha >1$, and let $W( x) =\exp ( -\vert x\vert ^{\alpha }) $, $x\in \mbox{\smallbf R}$. Let $\psi \in L_{\infty }(\mbox{\smallbf R}) $ be positive on a set of positive measure. For $n\geq 1$, one may form Sobolev orthonormal polynomials $( q_{n}) $, associated with the Sobolev inner product \[ ( f,g) =\int_{\mbox{\scriptsize\bf R}}fg( \psi W) ^{2}+\lambda \int_{\mbox{\scriptsize\bf R}}f^{\prime }g^{\prime }W^{2}. \] We establish strong asymptotics for the $( q_{n}) $ in terms of the ordinary orthonormal polynomials $( p_{n}) $ for the weight $W^{2}$, on and off the real line. More generally, we establish a close asymptotic relationship between $( p_{n}) $ and $( q_{n}) $ for exponential weights $W=\exp ( -Q) $ on a real interval $I$, under mild conditions on $Q$. The method is new and will apply to many situations beyond that treated in this paper.en
dc.description.sponsorshipThe work by F. Marcellan has been supported by Dirección General de Investigación (Ministerio de Ciencia y Technología) of Spain under grant BFM 2003-06335-C03-07, as well as NATO Collaborative grant PST.CLG 979738. J. Geronimo and D. Lubinsky, respectively, acknowledge support by NSF grants DMS-0200219 and DMS-0400446.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationConstructive Approximation, 2005, vol. 22, n. 3, p. 309-346
dc.identifier.doi10.1007/s00365-004-0578-1
dc.identifier.issn0176-4276 (Print)
dc.identifier.issn1432-0940 (Online)
dc.identifier.urihttps://hdl.handle.net/10016/5950
dc.language.isoeng
dc.publisherSpringer
dc.relation.publisherversionhttp://dx.doi.org/10.1007/s00365-004-0578-1
dc.rights© Springer
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherOrthogonal polynomials
dc.subject.otherSobolev norms
dc.subject.otherAsymptotics
dc.titleAsymptotics for Sobolev orthogonal polynomials for exponential weights
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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