Abstract
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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Communicated by Jan Derezinski.
SM and LP were partially supported by the EPSRC grant EP/ F029721/1. SM was also supported by the Lundbeck Foundation and the European Research Council under the European Community’s Seventh Framework Program (FP7/2007–2013)/ERC grant agreement 202859. RS was partially supported by the NSF grant DMS-0901015. The authors would like to thank Gerassimos Barbatis for participation in preliminary discussions which led to this paper. SM would like to express his thanks for hospitality to the University of Athens and ESI Vienna, where part of this work was made.
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Morozov, S., Parnovski, L. & Shterenberg, R. Complete Asymptotic Expansion of the Integrated Density of States of Multidimensional Almost-Periodic Pseudo-Differential Operators. Ann. Henri Poincaré 15, 263–312 (2014). https://doi.org/10.1007/s00023-013-0246-8
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DOI: https://doi.org/10.1007/s00023-013-0246-8