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Stein-Tomas theorem for a torus and the periodic Schrödinger operator with singular potential


Author: I. Kachkovskiĭ
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 6.
Journal: St. Petersburg Math. J. 24 (2013), 939-948
MSC (2010): Primary 35J10
DOI: https://doi.org/10.1090/S1061-0022-2013-01273-8
Published electronically: September 23, 2013
MathSciNet review: 3097555
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Abstract | References | Similar Articles | Additional Information

Abstract: A discrete version of the Stein-Tomas theorem for a torus is proved, except for the endpoint case. The result makes it possible to establish the absolute continuity of the spectrum of the periodic Schrödinger operator with a $ \delta $-like potential concentrated on a hypersurface of nonzero curvature.


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Additional Information

I. Kachkovskiĭ
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskay ul. 3, Petrodvorets, St. Petersburg 198054, Russia
Email: ilya.kachkovskiy@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2013-01273-8
Keywords: Stein--Tomas theorem, Schr\"odinger operator, periodic coefficients, absolutely continuous spectrum
Received by editor(s): June 15, 2012
Published electronically: September 23, 2013
Article copyright: © Copyright 2013 American Mathematical Society

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