Geodesic
Absolute continuity of the spectrum of a~periodic Schr\"odinger operator in a~multidimensional cylinder
Algebra i analiz, Tome 21 (2009) no. 1, pp. 133-152.

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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.
Keywords: absolute continuity of the spectrum, Schrödinger operator, periodic coefficients. 
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I. Kachkovskii; N. Filonov. Absolute continuity of the spectrum of a~periodic Schr\"odinger operator in a~multidimensional cylinder. Algebra i analiz, Tome 21 (2009) no. 1, pp. 133-152. http://geodesic.mathdoc.fr/item/AA_2009_21_1_a4/

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