Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6065

 Google™ Scholar. Others By: Branquinho, A. - Moreno, Ana F. - Marcellán, Francisco
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 Title: Asymptotic behaviour of Sobolev-type orthogonal polynomials on a rectifiable Jordan arc Author(s): Branquinho, A.Moreno, Ana F.Marcellán, Francisco Publisher: Springer Issued date: Oct-2002 Citation: Constructive Approximation, 2002, vol. 18, n. 2, p. 161-182 URI: http://hdl.handle.net/10016/6065 ISSN: 0176-4276 (Print)1432-0940 (Online) DOI: 10.1007/s00365-001-0005-9 Description: 22 pages, no figures.-- MSC2000 codes: Primary 42C05.MR#: MR1890494 (2002m:42023)Zbl#: Zbl 0991.42018 Abstract: Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product $$\langle f, g \rangle = \int_{E} f(\xi) \overline{g(\xi)} \rho (\xi) \xi f(Z) A g(Z) ,$$ 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, $M=l_{1} + \cdots + l_{m} + m$, $\xi denotes the arc length measure,$\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\$. Sponsor: 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. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1007/s00365-001-0005-9 Keywords: Orthogonal polynomialsSobolev inner productsAsymptoticsJordan curves Rights: © Springer Appears in Collections: DM - GAMA - Artículos de Revistas