St. Petersburg Mathematical Society

Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder

Author(s): I. Kachkovskiĭ; 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
Posted: November 5, 2009
Retrieve article in: PDF

Abstract: The Schrödinger operator $-\Delta + V$ in a

-dimensional cylinder, $d \ge 3$ , is considered with various boundary conditions. Under the assumption that the potential

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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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: 10.1090/S1061-0022-09-01087-5
PII: S 1061-0022(09)01087-5
Keywords: Absolute continuity of the spectrum, Schr\"odinger operator, periodic coefficients
Received by editor(s): 6/AUG/2008
Posted: 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).
Copyright of article: Copyright 2009, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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