# Sobolev-type orthogonal polynomials on the unit circle

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 dc.contributor.author Marcellán Español, Francisco José dc.contributor.author Moral, Leandro dc.date.accessioned 2009-12-15T13:05:48Z dc.date.available 2009-12-15T13:05:48Z dc.date.issued 2002-05-25 dc.identifier.bibliographicCitation Applied Mathematics and Computation, 2002, vol. 128, n. 2-3, p. 329-363 dc.identifier.issn 0096-3003 dc.identifier.uri http://hdl.handle.net/10016/6068 dc.description 35 pages, no figures.-- MSC2000 codes: 42C05. dc.description MR#: MR1891026 (2003e:42037) dc.description Zbl#: Zbl 1033.42025 dc.description.abstract This 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.sponsorship The 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.format.mimetype application/pdf dc.language.iso eng dc.publisher Elsevier dc.rights © Elsevier dc.subject.other Orthogonal polynomials dc.subject.other Reflection parameters dc.subject.other Nevai class dc.subject.other Sobolev inner products dc.title Sobolev-type orthogonal polynomials on the unit circle dc.type article dc.type.review PeerReviewed dc.description.status Publicado dc.relation.publisherversion http://dx.doi.org/10.1016/S0096-3003(01)00079-0 dc.subject.eciencia Matemáticas dc.identifier.doi 10.1016/S0096-3003(01)00079-0 dc.rights.accessRights openAccess
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