In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals $u_{0}$ and $u_{1}$. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of …
In this contribution, we study properties of block Hessenberg matrices associated with matrix orthonormal polynomials on the unit circle. We also consider the Uvarov and Christoffel spectral matrix transformations of the orthogonality measure, and …
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 …
Given a normalized measure mu supported on [-1,1], a measure sigma supported on the unit circle can be defined by using the so-called Szego transformation. This also establishes a well known relation between the corresponding Stieltjes and …
Given a perturbation of a matrix measure supported on the unit circle, we analyze the perturbation obtained on the corresponding matrix measure on the real line, when both measures are related through the Szegő matrix transformation. Moreover, using …