Absolute continuity of the spectrum of a periodic Schrödinger operator in a multidimensional cylinder

The Schrödinger operator $-\Delta+V$ in a $d$-dimensional cylinder, $d\ge 3$, is considered with various boundary conditions. Under the assumption that the potential $V$ is periodic with respect to the “longitudinal” variables and $V\in L_{d-1,\mathrm{loc}}$, it is proved that the spectrum of the Schrödinger operator is absolutely continuous.