Relative Asymptotics for Orthogonal Matrix Polynomials with Convergent Recurrence Coefficients Original Research Article

The asymptotic behavior of γn(dβ) γn(dα)−1 and Pn(x, dβ) P−1n(x, dα) is studied. Here (γn(.))n are the leading coefficients of the orthonormal matrix polynomials Pn(x, .) with respect to the matrix measures dβ and dα which are related by dβ(u)=dα(u)+∑Nk=1 Mk δ(u−ck), where Mk are positive definite matrices, δ is the Dirac measure and ck lies outside the support of dα for k=1, …, N. Finally, we deduce the asymptotic behavior of Pn(c, dβ) MP*n(c, dα) when dβ(u)=dα(u)+Mδ(u−c), with M a positive definite matrix and c outside the support of dα.