On Spectral Deformations and Singular Weyl Functions for One-Dimensional 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.

13 pages

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Cited by in corpus (4)

• Spectral asymptotics for canonical systems
• Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions
• Generalized wave operators: dynamical and stationary cases and divergence problem
• On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications