Relative Asymptotics of Matrix Orthogonal Polynomials for Uvarov Perturbations: The Degenerate Case

Let be a square matrix of measures, and the associated sequence of orthonormal matrix polynomials satisfying the three-term recurrence relation Let , where is a positive definite matrix, is the Dirac measure supported at that is located outside the support of . We study the outer relative asymptotics of the sequence with respect to the sequence under quite general assumption on the coefficients of the three-term recurrence relation and {B-n (alpha)}(n >= 0).