Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle
Hossain Oulad Yakhlef, Francisco Marcellán · Analysis in Theory and Applications · 2002
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.