Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators

TL;DR

This paper develops a spectral theory for one-dimensional Dirac operators, establishing key existence and uniqueness results, and applies these findings to radial Dirac operators.

Contribution

It introduces a singular Weyl-Titchmarsh-Kodaira framework for Dirac operators, including spectral transformation and uniqueness theorems, with applications to radial cases.

Findings

Established existence of spectral transformation.

Proved local Borg-Marchenko and Hochstadt-Liebermann type uniqueness results.

Applied theory to radial Dirac operators.

Abstract

We develop singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators. In particular, we establish existence of a spectral transformation as well as local Borg-Marchenko and Hochstadt-Liebermann type uniqueness results. Finally, we give some applications to the case of radial Dirac operators.