Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/5977

 Google™ Scholar. Others By: Cachafeiro, Alicia - Marcellán, Francisco - Moreno Balcázar, Juan José
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 Title: On asymptotic properties of Freud–Sobolev orthogonal polynomials Author(s): Cachafeiro, AliciaMarcellán, FranciscoMoreno Balcázar, Juan José Publisher: Elsevier Issued date: Nov-2003 Citation: Journal of Approximation Theory, 2004, vol. 125, n. 1, p. 26-41 URI: http://hdl.handle.net/10016/5977 ISSN: 0021-9045 DOI: 10.1016/j.jat.2003.09.003 Description: 16 pages, no figures.-- MSC2000 codes: 33C45; 33C47; 42C05.MR#: MR2016838 (2005e:33004)Zbl#: Zbl 1043.33005 Abstract: In this paper we consider a Sobolev inner product $(f,g)_S=\int fg\,d\mu+ \lambda \int f'g'\,d\mu (*)$, and we characterize the measures μ for which there exists an algebraic relation between the polynomials, {Pn}, orthogonal with respect to the measure μ and the polynomials, {Qn}, orthogonal with respect to (*), such that the number of involved terms does not depend on the degree of the polynomials. Thus, we reach in a natural way the measures associated with a Freud weight. In particular, we study the case $d\mu=e -x }dx$ supported on the full real axis and we analyze the connection between the so-called Nevai polynomials (associated with the Freud weight $e -x }$)and the Sobolev orthogonal polynomials Qn. Finally, we obtain some asymptotics for {Qn}. Sponsor: Research by first author (A.C.) partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under Grant BFM 2000 0015. Research by second author (F.M.) partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under Grant BFM2003 06335 C03 02, by INTAS Project 2000 272 and by the NATO collaborative Grant PST.CLG. 979738. Research by third author (J.J.M.-B.) partially supported by Junta de Andalucía, Grupo de Investigación FQM 0229, Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under Grant BFM 2001 3878 C02 02 and INTAS Project 2000 272. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/j.jat.2003.09.003 Keywords: Sobolev orthogonal polynomialsFreud polynomialsAsymptotics Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas