# Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators

@article{Morozov2012CompleteAE,
title={Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators},
author={Sergey Morozov and Leonid Parnovski and Roman Shterenberg},
journal={Annales Henri Poincar{\'e}},
year={2012},
volume={15},
pages={263-312}
}
• Published 4 April 2012
• Mathematics
• Annales Henri Poincaré
We obtain a complete asymptotic expansion of the integrated density of states of operators of the form $${H = (-\Delta)^w+ B}$$ in $${\mathbb{R}^d}$$ . Here w >  0 and B belong to a wide class of almost-periodic self-adjoint pseudo-differential operators of order less than 2w. In particular, we obtain such an expansion for magnetic Schrödinger operators with either smooth periodic or generic almost-periodic coefficients.
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We obtain a complete asymptotic expansion of the integrated density of states of operators of the form $${H = (-\Delta)^w+ B}$$ in $${\mathbb{R}^d}$$ . Here w > 0 and B belong to a wide class of
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