On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators

TL;DR

This paper explores the relationship between spectral deformations and Weyl functions for one-dimensional Dirac operators, providing explicit formulas and applying results to radial cases with implications for spectral theory.

Contribution

It establishes a connection between singular Weyl functions and the double commutation method for Dirac operators, including explicit computations and spectral class characterizations.

Findings

Derived the singular Weyl function of the commuted operator from the original data.

Showed the singular Weyl function for radial Dirac operators belongs to a generalized Nevanlinna class.

Applied spectral deformation techniques to analyze spectral properties of Dirac operators.

Abstract

We investigate the connection between singular Weyl-Titchmarsh-Kodaira theory and the double commutation method for one-dimensional Dirac operators. In particular, we compute the singular Weyl function of the commuted operator in terms of the data from the original operator. These results are then applied to radial Dirac operators in order to show that the singular Weyl function of such an operator belongs to a generalized Nevanlinna class $N_{\kappa_0}$ with $\kappa_0=\lfloor|\kappa| + \frac{1}{2}\rfloor$, where $\kappa\in \mathbb{R}$ is the corresponding angular momentum.