Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
First the authors recall the theory of matrix orthogonal polynomials on the unit circle, their recurrence relations, reproducing kernels, and the relation to unitary block Hessenberg matrices. Then the spectral transformations (Uvarov, Christoffel) known for the scalar case from e.g. [\textit{K. Castillo} et al., Suppl. Rend. Circ. Mat. Palermo (2) 82, 3--26 (2010; Zbl 1470.42050)] are also generalized to the block case.
matrix orthogonal polynomials on unit circle
scientific article; zbMATH DE number 7438346
scientific article