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...

Positive polynomial matrices play a fundamental role in systems and control theory. We give here a simplified proof of the fact that the convex set of positive polynomial matrices can be parameterized using block Hankel and block Toeplitz matrices. We also show how to derive efficient computational algorithms for optimization problems over positive pseudo polynomial matrices over the real line,...

In this paper, we consider the blind image restoration as a convex constrained problem and we propose to solve this problem by a conditional gradient method. Such a method is based on a Thikonov regularization technique and is obtained by an approximation of the blur matrix as a Kronecker product of two matrices given as a sum of a Toeplitz and a Hankel matrices. Numerical examples are given to...

We consider the question: To what extend does the Weyl function (i.e., the abstract Dirichlet-to-Neumann map) see the same singularities as the resolvent of some restriction of the maximal operator. The proper, so-called detectable, subspace will be introduced and analyzed for particular examples, such as, Schrodinger operators, Hain–Lust operators, and (if time permits), the Friedrichs model o...