Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrödinger operators

Abstract

We prove the complete asymptotic expansion of the integrated density of states of a Schrödinger operator $H=-\Delta+b$ acting in $\Bbb{R}^d$ when the potential $b$ is either smooth periodic, or generic quasi-periodic (finite linear combination of exponentials), or belongs to a wide class of almost-periodic functions.

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Authors

Leonid Parnovski

Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom

Roman Shterenberg

Department of Mathematics, University of Alabama at Birmingham, 1300 University Boulevard, Birmingham AL 35294-1170