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

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.