Relative asymptotics for orthogonal matrix polynomials with convergent recurrence coefficients

The asymptotic behavior of gamma (n)(d beta) gamma (n)(d alpha)(-1) and P-n (x, d beta) P-n(-1)(x, d alpha) is studied. Here (gamma (n)(.))(n) are the leading coefficients of the orthonormal matrix polynomials P-n(x,.) with re spect to the matrix measures d beta and d alpha which are related by d beta (u)= d alpha (u)+ Sigma (N)(k=1), M(k)delta (u - c(k)), where M-k are posi tive definite matrices, delta is the Dirac measure and c(k) lies outside th e support of d alpha for k = 1,..., N. Finally, we deduce the asymptotic be havior of P-n(c, d beta) MPn*(c, d alpha) when d beta (u) = d alpha (u) + M delta (u - c), with M a positive definite matrix and c outside the support of d alpha. (C) 2001 Academic Press.