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}
}
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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