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

Let α be a square matrix of measures, and {Pn(x;α)}n≥0 the associated sequence of orthonormal matrix polynomials satisfying the three-term recurrence relation xPn(x;α)=An+1(α)Pn+1(x;α)+Bn(α)Pn(x;α)+An*(α)Pn-1(x;α),n≥ 0. Let d β(u) = def d α(u) + Mδ(u- c) , where M is a positive definite matrix, δ(u- c) is the Dirac measure supported at c that is located outside the support of d α. We study the outer relative asymptotics of the sequence {Pn(x;β)}n≥0 with respect to the sequence {Pn(x;α)}n≥0 under quite general assumption on the coefficients of the three-term recurrence relation {An(α)}n≥0 and {Bn(α)}n≥0.