On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems

Abstract

A new class of the structured matrices related to the discrete skew-self-adjoint Dirac systems is introduced. The corresponding matrix identities and inversion procedure are treated. Analogs of the Schur coefficients and of the Christoffel-Darboux formula are studied. It is shown that the structuredmatrices from this class are always positive-definite, andapplications for an inverse problem for the discrete skew-self-adjoint Dirac system are obtained.