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Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder


Authors: I. Kachkovskiĭ and N. Filonov
Translated by: the authors
Original publication: Algebra i Analiz, tom 21 (2009), nomer 1.
Journal: St. Petersburg Math. J. 21 (2010), 95-109
MSC (2000): Primary 35P05
DOI: https://doi.org/10.1090/S1061-0022-09-01087-5
Published electronically: November 5, 2009
MathSciNet review: 2553054
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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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Additional Information

I. Kachkovskiĭ
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: ilya.kachkovskiy@gmail.com

N. Filonov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: filonov@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-09-01087-5
Keywords: Absolute continuity of the spectrum, Schr\"odinger operator, periodic coefficients
Received by editor(s): August 6, 2008
Published electronically: November 5, 2009
Additional Notes: The research of the first author was supported by EPSRC (grant GR/T25552/01) and by RFBR (grant no. 08-01-00209-a).
Article copyright: © Copyright 2009 American Mathematical Society

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