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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.Comment: to appear in the Proceedings of the 'Spectral Days' conference, Santiago de Chile 201

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