Stability of Dirac resonances

TL;DR

This paper establishes the stability and continuous dependence of Dirac resonances and related functions on compactly supported potential perturbations, ensuring robustness of spectral properties under small changes.

Contribution

It proves the closure of Dirac resonances under  perturbations and demonstrates the continuous dependence of potentials and associated functions, advancing spectral stability theory.

Findings

Resonances form a closed set under  perturbations.

Potential depends continuously on perturbations.

Results extend to Jost and Hermite-Biehler functions.

Abstract

We prove that the class of resonances of Dirac operators on the half-line with compactly supported potentials is closed with respect to $\ell^1$ 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.