Computational Methods and Function Theory ( IF 0.738 ) Pub Date : 2020-06-29 , DOI: 10.1007/s40315-020-00324-x
H. Dueñas, E. Fuentes, L. E. Garza

Let $$\sigma$$ be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of $$\sigma$$ defined by \begin{aligned} d\sigma _{c_m}(z)=W_m(z)^Hd\sigma (z)W_m(z), \end{aligned} where $$W_m(z)=\prod _{j=1}^m(z\mathbf{I} -A_j)$$ and $$A_j$$ is a square matrix for $$j=1,\ldots ,m.$$ Moreover, we study the relative asymptotics of the associated orthogonal matrix polynomials when $$\sigma _{c_m}$$ satisfies a matrix condition in the diagonal case. Some illustrative examples are considered.

down
wechat
bug