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Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

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ISSN: 1000-9221 (Print)
ISSN: 1573-8175 (Online)
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2002-12
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Springer
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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.
Description
19 pages, no figures.-- MSC2000 codes: 42C05, 47A56.
MR#: MR1970413 (2004b:42058)
Zbl#: Zbl 1047.42021
Keywords
Matrix orthogonal polynomials, Szegö condition, Comparative asymptotics
Bibliographic citation
Approximation Theory and its Applications, 2002, vol. 18, n. 4, p. 1-19