Discrete Self-adjoint Dirac Systems: Asymptotic Relations, Weyl Functions and Toeplitz Matrices

We consider discrete Dirac systems as an approach to the study of corresponding block Toeplitz matrices, which in many ways completes famous via Szegő recurrences and matrix orthogonal polynomials. prove analog Christoffel–Darboux formula derive asymptotic relations for reproducing kernel (using Weyl–Titchmarsh functions systems). These are expressed also terms matrices. case rational (and GBDT version Bäcklund–Darboux transformation trivial system) well. It is shown that diagonal plus semi-separable matrices (which easily inverted) appear this case.