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Sobolev-type orthogonal polynomials on the unit circle

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorMarcellán Español, Francisco José
dc.contributor.authorMoral, Leandro
dc.date.accessioned2009-12-15T13:05:48Z
dc.date.available2009-12-15T13:05:48Z
dc.date.issued2002-05-25
dc.description35 pages, no figures.-- MSC2000 codes: 42C05.
dc.descriptionMR#: MR1891026 (2003e:42037)
dc.descriptionZbl#: Zbl 1033.42025
dc.description.abstractThis paper deals with polynomials orthogonal with respect to a Sobolev-type inner product $$ \langle f,g\rangle =\int_{-\pi}^\pi f(e^{i\theta}) \overline{g(e^{i\theta})} d\mu(e^{i\theta})\, + \, \bold{f}(c)A (\bold{g}(c))^H.$$ where μ is a positive Borel measure supported on [−π,π), A is a nonsingular matrix and 1. We denote f(c)=(f(c),f'(c),\dots,f^{(p)}(c)) and v^H the transposed conjugate of the vector v. We establish the connection of such polynomials with orthogonal polynomials on the unit circle with respect to the measure [see attached full-text file]. Finally, we deduce the relative asymptotics for both families of orthogonal polynomials.
dc.description.sponsorshipThe work of the first author (F. Marcellán) was partially supported by D.G.E.S. of Spain under grant PB96-0120-C03-01. The work of the second author (L. Moral) was partially supported by P.A.I. 1997 (Universidad de Zaragoza) CIE-10.
dc.description.statusPublicado
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationApplied Mathematics and Computation, 2002, vol. 128, n. 2-3, p. 329-363
dc.identifier.doi10.1016/S0096-3003(01)00079-0
dc.identifier.issn0096-3003
dc.identifier.urihttps://hdl.handle.net/10016/6068
dc.language.isoeng
dc.publisherElsevier
dc.relation.publisherversionhttp://dx.doi.org/10.1016/S0096-3003(01)00079-0
dc.rights© Elsevier
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticas
dc.subject.otherOrthogonal polynomials
dc.subject.otherReflection parameters
dc.subject.otherNevai class
dc.subject.otherSobolev inner products
dc.titleSobolev-type orthogonal polynomials on the unit circle
dc.typeresearch article*
dc.type.reviewPeerReviewed
dspace.entity.typePublication
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