Absence of Eigenvalues for the Periodic Schrödinger Operator with Singular Potential in a Rectangular Cylinder

We consider the periodic Schrödinger operator on a $d$-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form $\sigma(x,y)\delta_{\Sigma}(x,y)$, where $\Sigma$ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that $\Sigma$ is sufficiently smooth and $\sigma\in L_{p,\operatorname{loc}}(\Sigma)$, $p>d-1$.