Stability of Dirac resonances

We prove that the class of resonances of Dirac operators on the half-line with compactly supported potentials is closed with respect to ${\mathrm{\ell }}^1$ perturbations. We also prove that the potential depends continuously on such perturbations. We show that similar results hold true for the Jost functions and Hermite-Biehler functions associated with Dirac operators.