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

Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables

Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schr\"odinger equations depending on two variables and of nonlinear wave equations depending on three variables