Complete asymptotic expansion of the spectral function of multidimensional almost-periodic Schrödinger operators

Abstract

We prove the existence of a complete asymptotic expansion of the spectral function (the integral kernel of the spectral projection) of a Schrödinger operator $H=-\Delta +b$ acting in ${\mathbb{R}}^d$ when the potential $b$ is real and either smooth periodic, or generic quasiperiodic (finite linear combination of exponentials), or belongs to a wide class of almost-periodic functions.