# Asymptotic behaviour of Sobolev-type orthogonal polynomials on a rectifiable Jordan arc

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 dc.contributor.author Branquinho, A. dc.contributor.author Moreno, Ana F. dc.contributor.author Marcellán Español, Francisco José dc.date.accessioned 2009-12-15T12:31:09Z dc.date.available 2009-12-15T12:31:09Z dc.date.issued 2002-10 dc.identifier.bibliographicCitation Constructive Approximation, 2002, vol. 18, n. 2, p. 161-182 dc.identifier.issn 0176-4276 (Print) dc.identifier.issn 1432-0940 (Online) dc.identifier.uri http://hdl.handle.net/10016/6065 dc.description 22 pages, no figures.-- MSC2000 codes: Primary 42C05. dc.description MR#: MR1890494 (2002m:42023) dc.description Zbl#: Zbl 0991.42018 dc.description.abstract Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product $$\langle f, g \rangle = \int_{E} f(\xi) \overline{g(\xi)} \rho (\xi) \xi \xi f(Z) A g(Z)^H,$$ where $E$ is a rectifiable Jordan curve or arc in the complex plane $$f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)),$$ $A$ is an $M \times M$ Hermitian matrix, $M=l_{1} + \cdots + l_{m} + m$, $denotes the arc length measure,$\rho$is a nonnegative function on$E$, and$z_{i} \in \Omega$,$i=1,2,\ldots,m$, where$\Omega$is the exterior region to$E\$. dc.description.sponsorship The work of the first author was supported by the Portuguese Ministry of Science and Technology, Fundação para a Ciência e Tecnología of Portugal under grant FMRH-BSAB-109-99 and by the Centro de Matemática da Universidade de Coimbra. The second author would also like to thank the Unidade de Investigação (Matemática e Aplicações) of the University of Aveiro for their support. The work of the second and third authors was supported by the Dirección General de Enseñanza Superior (DGES) of Spain under grant PB 96-0120-C03-01. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Springer dc.rights © Springer dc.subject.other Orthogonal polynomials dc.subject.other Sobolev inner products dc.subject.other Asymptotics dc.subject.other Jordan curves dc.title Asymptotic behaviour of Sobolev-type orthogonal polynomials on a rectifiable Jordan arc dc.type article dc.type.review PeerReviewed dc.description.status Publicado dc.relation.publisherversion http://dx.doi.org/10.1007/s00365-001-0005-9 dc.subject.eciencia Matemáticas dc.identifier.doi 10.1007/s00365-001-0005-9 dc.rights.accessRights openAccess
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