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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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Analysis in Theory and Applications

Abstract

Given a positive definite matrix measure Ω supported on the unit circleT, then main purpose of this paper is to study the asymptotic behavior of\(L_R \left( {\tilde \Omega } \right)L_R \left( \Omega \right)^{ - 1} \) and\(\Phi _R \left( {z;\tilde \Omega } \right)\Phi _R \left( {z;\tilde \Omega } \right)^{ - 1} \) where

$$\tilde \Omega \left( z \right) = \Omega \left( z \right) + $$

M

$$\tilde \Omega \left( z \right) = \Omega \left( z \right) + $$

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\(\Phi _n \left( {w;\tilde \Omega } \right)\Phi _n \left( {w;\tilde \Omega } \right)\) in the case whenM=I.

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Authors and Affiliations

  1. Departmento De Matemática Aplicada, Universidad De Granada, C/Severo Ochoa, S/N 18071, Granada, Spain

    Hossain O. Yakhlef

  2. Departamento de Matemáticas, Universidad Carlos I de Madrid, C/Batarque, 15, 28911, Leganés, Spain

    Francisco Marcellán

Authors
  1. Hossain O. Yakhlef
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  2. Francisco Marcellán
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Correspondence to Hossain O. Yakhlef.

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Yakhlef, H.O., Marcellán, F. Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle. Approx. Theory & its Appl. 18, 1–19 (2002). https://doi.org/10.1007/BF02845271

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