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

TL;DR

This paper derives a comprehensive asymptotic expansion for the integrated density of states of multidimensional almost-periodic pseudo-differential operators, including magnetic Schrödinger operators, advancing spectral analysis in mathematical physics.

Contribution

It provides the first complete asymptotic expansion for the integrated density of states of a broad class of almost-periodic pseudo-differential operators, including magnetic Schrödinger operators.

Findings

Established a full asymptotic expansion for the integrated density of states.

Extended results to magnetic Schrödinger operators with periodic or almost-periodic coefficients.

Enhanced understanding of spectral properties of multidimensional almost-periodic operators.

Abstract

We obtain a complete asymptotic expansion of the integrated density of states of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs 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 Schr\"odinger operators with either smooth periodic or generic almost-periodic coefficients.