Stein–Tomas theorem for a torus and the periodic Schrödinger operator with singular potential
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I. Kachkovskiĭ
Translated by: the author - St. Petersburg Math. J. 24 (2013), 939-948
- DOI: https://doi.org/10.1090/S1061-0022-2013-01273-8
- Published electronically: September 23, 2013
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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.References
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Bibliographic 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
- Received by editor(s): June 15, 2012
- Published electronically: September 23, 2013
- © Copyright 2013 American Mathematical Society
- Journal: St. Petersburg Math. J. 24 (2013), 939-948
- MSC (2010): Primary 35J10
- DOI: https://doi.org/10.1090/S1061-0022-2013-01273-8
- MathSciNet review: 3097555