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

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

2010-11-05

arxiv.org/abs/1011.1394v1

Mathematics

Spectral Theory

LaTeX, 10 pages, preprint. Russian version is to appear in "Zapiski Nauchnykh Seminarov POMI", English translation will be pub

Scientific paper

We consider the Schr\"odinger 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.

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