On the Regularity of the Hausdorff Distance Between Spectra of Perturbed Magnetic Hamiltonians

Abstract

We study the regularity properties of the Hausdorff distance between spectra of continuous Harper-like operators. As a special case we obtain H\"{o}lder continuity of this Hausdorff distance with respect to the intensity of the magnetic field for a large class of magnetic elliptic (pseudo)differential operators with long range magnetic fields.