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

On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians