Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder

Abstract

We consider the periodic Schrodinger operator on a d-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form σ(x, y)δΣ(x,y), where Σ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that Σ is sufficiently smooth and σ ∈ Lp,loc(Σ), p > d − 1.