Recovery of Dirac system from the rectangular Weyl matrix function

TL;DR

This paper develops inverse problem techniques for Dirac systems with rectangular matrix potentials, analyzing their Weyl functions, deriving high energy asymptotics, and establishing uniqueness results, extending classical theories to non-square cases.

Contribution

It introduces new inverse problem solutions for Dirac systems with rectangular potentials, expanding classical Weyl theory to non-square matrix functions.

Findings

Weyl functions are non-expansive in the upper semi-plane.

High energy asymptotics of Weyl functions are derived.

Borg-Marchenko type uniqueness results are established.

Abstract

Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are treated for such Weyl functions, and some results are new even for the square Weyl functions. High energy asymptotics of Weyl functions and Borg-Marchenko type uniqueness results are derived too.