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

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Show simple item record Branquinho, A. Moreno, Ana F. Marcellán Español, Francisco José 2009-12-15T12:31:09Z 2009-12-15T12:31:09Z 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.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 PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1007/s00365-001-0005-9
dc.rights.accessRights openAccess
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