This article is cited in 2 papers

Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices

A. E. Choke Rivero^a, L. E. Garza Gaona<sup>b

a</sup> Universidad Michoacana de San Nicolás de Hidalgo, C. U. Building, C. P. 58030, Morelia, México
^b University of Colima, 340 Bernal Díaz del Castillo, 28045 Colima, México

Abstract: Let $\{c_j\}_{j=0}^{n}$ be a sequence of matrix moments associated with a matrix of measures supported on the unit circle, and let $\{P_j\}_{j=0}^{n}$ be its corresponding sequence of monic matrix orthogonal polynomials. In this contribution, we consider a perturbation on the moments and find an explicit relation for the perturbed orthogonal polynomials in terms of $\{P_j\}_{j=0}^{n}$. We also obtain an expression for the corresponding second kind polynomials.

Keywords: matrix orthogonal polynomials on the unit circle, moment problem, second kind polynomials, Toeplitz matrices.

UDC: 517.538

Received: 06.07.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:12, 57–69

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