J. Math. Phys. 56, 012102 (2015) [DOI: 10.1063/1.4905166]

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

Alexander Beigl, Jonathan Eckhardt, Aleksey Kostenko, and Gerald Teschl

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 Nκ0 with κ0=⌊|κ| + 1/2 ⌋, where κ∈ ℝ is the corresponding angular momentum.

MSC2010: Primary 34B20, 34L40; Secondary 34L05, 34B30
Keywords: Dirac operators, spectral theory

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