Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder

Kachkovskiĭ, I.; Filonov, N.

doi:10.1090/S1061-0022-09-01087-5

Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder
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by I. Kachkovskiĭ and N. Filonov
Translated by: the authors

St. Petersburg Math. J. 21 (2010), 95-109

DOI: https://doi.org/10.1090/S1061-0022-09-01087-5

Published electronically: November 5, 2009

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Abstract:

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 $V \in L_{d-1, \operatorname {loc}}$, it is proved that the spectrum of the Schrödinger operator is absolutely continuous.

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