Dynamical and spectral Dirac systems: response function and inverse problems

TL;DR

This paper links response functions of dynamical Dirac systems with spectral data, enabling new methods for system recovery and explicit solution construction.

Contribution

It introduces a novel connection between dynamical and spectral Dirac systems, providing a rigorous procedure for system recovery from response functions.

Findings

Established connections between response functions and spectral data.

Proposed a new method for recovering dynamical Dirac systems.

Constructed explicit solutions for the inverse problem.

Abstract

We establish simple connections between response functions of the dynamical Dirac systems and $A$-amplitudes and Weyl functions of the spectral Dirac systems. Using these connections we propose a new and rigorous procedure to recover a general-type dynamical Dirac system from its response function as well as a procedure to construct explicit solutions of this problem.