Matrix Uvarov Transformation on the Unit Circle: Asymptotic Properties

Abstract

Let σ be an l× l Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of matrix orthogonal polynomials associated with the Uvarov matrix transformation of σ defined by dσum(z)=dσ(z)+∑j=1mMjδ(z-ζj),where Mj is an l× l positive definite matrix, ζj∈ C with ζj≠ ζi and δ is the Dirac matrix measure.