On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
arXiv:1410.1152 · doi:10.1063/1.4905166
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 $N_{κ_0}$ with $κ_0=\lfloor|κ| + \frac{1}{2}\rfloor$, where $κ\in \mathbb{R}$ is the corresponding angular momentum.
13 pages