Weyl matrix functions and inverse problems for discrete Dirac type self-adjoint system: explicit and general solutions

TL;DR

This paper studies discrete Dirac type self-adjoint systems, providing explicit solutions for inverse problems, and establishing connections with block Toeplitz matrices, thereby advancing understanding of their spectral properties.

Contribution

It offers explicit solutions to inverse problems for discrete Dirac systems and links these systems to block Toeplitz matrices, extending classical results.

Findings

Representation of the fundamental solution is obtained.

Inverse problems on the interval and semi-axis are solved.

A Borg-Marchenko type result is established.

Abstract

Discrete Dirac type self-adjoint system is equivalent to the block Szeg\"o recurrence. Representation of the fundamental solution is obtained, inverse problems on the interval and semi-axis are solved. A Borg-Marchenko type result is obtained too. Connections with the block Toeplitz matrices are treated.