Inverse resonance scattering for Dirac operators on the half-line
Mathematical Physics
2020-09-15 v2 math.MP
Spectral Theory
Abstract
We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function and prove that a potential is uniquely determined by its resonances. Moreover, we prove the following: 1) resonances are free parameters and a potential continuously depends on a resonance, 2) the forbidden domain for resonances is estimated, 3) asymptotics of resonance counting function is determined, 4) these results are applied to canonical systems.
Cite
@article{arxiv.2003.12502,
title = {Inverse resonance scattering for Dirac operators on the half-line},
author = {Evgeny Korotyaev and Dmitrii Mokeev},
journal= {arXiv preprint arXiv:2003.12502},
year = {2020}
}