Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur coefficients and structured matrices are treated. Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semiaxis are solved.Comment: Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplifie

Extremal classical interpolation problems (matrix case)

AbstractIn this paper, we try to find amongst the solutions w(z) of the corresponding interpolation problem the solution which satisfies an additional extremal condition. We show that degenerate interpolation problems play an important role in the theory of extremal interpolation problems. At the end of the paper we accomplish a comparison of our approach with former known approaches