A class of matrix orthogonal polynomials on the unit circle

AbstractThe study of matrix orthogonal polynomials on the unit circle is connected with problems of applied mathematics such as filtering theory, prediction theory, and scattering theory. In this paper, some families of matrix orthogonal polynomials on the unit circle are given explicitly. The decomposition ∏ = ∏(A(z)) ⊕ z∏(A(z)) ⊕ ⋯ ⊕ zh−1 ∏(A(z)), where ∏ is the linear space of complex algebraic polynomials, is the main idea for this approach