Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions

TL;DR

This paper investigates discrete Dirac systems on the semiaxis, deriving explicit formulas for reflection coefficients and demonstrating the equivalence of rational reflection coefficients and Weyl functions in both self-adjoint and skew-self-adjoint cases.

Contribution

It provides explicit expressions for reflection coefficients and establishes the coincidence of rational reflection coefficients and Weyl functions for discrete Dirac systems.

Findings

Explicit formulas for reflection coefficients derived

Rational reflection coefficients and Weyl functions are shown to coincide

Results apply to both self-adjoint and skew-self-adjoint cases

Abstract

We consider the cases of the self-adjoint and skew-self-adjoint discrete Dirac systems, obtain explicit expressions for reflection coefficients and show that rational reflection coefficients and Weyl functions coincide.