Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices (Q1703184)

Let \(\{c_j\}_{j=0}^n\) be a sequence of matrix moments associated with a matrix of measure supported on the unit circle in \(\mathbb{C}\), and let \(\{P_j\}_{j=0}^n\) be the corresponding sequence of monic matrix orthogonal polynomials. The authors consider a perturbation of the moments and find an explicit relation for the perturbed orthogonal polynomials in terms of \(\{P_j\}_{j=0}^n\). The approach of \textit{A. V. Efimov} and \textit{V. P. Potapov} [Russ. Math. Surv. 28, No. 1, 69--140 (1973; Zbl 0285.94009)] plays an important role in this development. See [\textit{A. E. Choque-Rivero} and \textit{L. E. Garza}, Integral Transforms Spec. Funct. 26, No. 3, 177--191 (2015; Zbl 1316.42030);\textit{K. Castillo} et al., Appl. Math. Comput. 221, 444--452 (2013; Zbl 1329.15057)] for analogue problems for sequences of matrix moments associated with orthogonality measure with support on the real line.