Relative Asymptotics for Orthogonal Matrix Polynomials with Convergent Recurrence Coefficients

The asymptotic behavior of #n (d;) #n (d:) and Pn (x, d;) P n (x, d:) is studied. Here (#n (.))n are the leading coefficients of the orthonormal matrix polynomials Pn (x, .) with respect to the matrix measures d; and d: which are related by d;(u)= d:(u)+ k=1 Mk$(u&ck), where Mk are positive definite matrices, $ is the Dirac measure and ck lies outside the support of d: for k=1, ..., N. Finally, we deduce the asymptotic behavior of Pn (c, d;) MPn*(c, d:) when d;(u)=d:(u)+M$(u&c), with M a positive definite matrix and c outside the support of d:. 2001 Academic Press