Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder

Abstract

We consider the Schrödinger operator $H=-\Delta +V$ in a layer or in a $d$-dimensional cylinder. The potential $V$ is assumed to be periodic with respect to some lattice. We establish the absolute continuity of $H$, assuming $V \in L_{p, \loc}$, where $p$ is a real number greater than $d/2$ in the case of a layer, and $p>\max (d/2,d-2)$ for the cylinder.

LaTeX, 10 pages, preprint. Russian version is to appear in "Zapiski Nauchnykh Seminarov POMI", English translation will be published in "Journal of Mathematical Sciences", Springer

References in corpus (1)

• On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator