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

TL;DR

This paper develops a transfer matrix framework for discrete Dirac systems with rectangular coefficients, linking them to Szeg"o recurrence and solving inverse problems with uniqueness guarantees.

Contribution

It introduces a transfer matrix representation for discrete Dirac systems with rectangular coefficients and solves inverse problems with uniqueness theorems.

Findings

Transfer matrix function representation of fundamental solutions.

Connections established with Szeg"o recurrence and structured matrices.

Inverse problems on interval and semiaxis are solved.

Abstract

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.