Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6319

 Google™ Scholar. Others By: Yakhlef, Hossain O. - Marcellán, Francisco
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 Title: Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle Author(s): Yakhlef, Hossain O.Marcellán, Francisco Publisher: Springer Issued date: Dec-2002 Citation: Approximation Theory and its Applications, 2002, vol. 18, n. 4, p. 1-19 URI: http://hdl.handle.net/10016/6319 ISSN: 1000-9221 (Print)1573-8175 (Online) DOI: 10.1007/BF02845271 Description: 19 pages, no figures.-- MSC2000 codes: 42C05, 47A56.MR#: MR1970413 (2004b:42058)Zbl#: Zbl 1047.42021 Abstract: Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of $L_n(\tilde{\Omega}) L_n(\Omega) -1}$ and $\Phi_n(z, \tilde{\Omega}) \Phi_n(z, \tilde{\Omega}) -1}$ where $\tilde{\Omega}(z) = \Omega(z) + M \delta ( z - w)$, $1$, M is a positive definite matrix and δ is the Dirac matrix measure. Here, Ln(·) means the leading coefficient of the orthonormal matrix polynomials Φn(z; •).Finally, we deduce the asymptotic behavior of $\Phi_n(omega, \tilde{\Omega}) \Phi_n(omega, \Omega)$ in the case when M=I. Sponsor: The work of the second author was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01 and INTAS Project INTAS93-0219 Ext. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1007/BF02845271 Keywords: Matrix orthogonal polynomialsSzegö conditionComparative asymptotics Rights: © Springer Appears in Collections: DM - GAMA - Artículos de Revistas