Stability of resonances for the Dirac operator

In this paper, we study the Dirac operator on the half-line with a compactly supported potential. Let $(k_n)_{n \geq 1}$ be a sequence of its resonances with multiplicity and arranged such that $|k_n|$ do not decrease as $n$ increases. We will prove that for any sequence $(r_n)_{n \geq 1} \in \ell^1$ such that the points $k_n + r_n$ remain in the lower half-plane for all $n \geq 1$,the sequence $(k_n + r_n)_{n \geq 1}$ is also a sequence of resonances of a similar operator.Moreover, we will prove that the potential of the Dirac operator changes continuously under such perturbations.