Eigensystems of Dirac operators with singular potentials

Abstract

We perturb one-dimensional Dirac operators on a bounded interval subject to Dirichlet boundary conditions by potentials with Fourier coefficients exhibiting power-decay. As a consequence of Paley-Zygmund theorem, this broad family of potentials comprises distributions that are neither integrable functions nor measures. We localize the spectrum of the perturbed operator and, as the main result, show that its eigensystem generates a Riesz basis.