Schrödinger operator on the axis with potentials depending on two parameters
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R. R. Gadyl′shin and I. Kh. Khusnullin
Translated by: B. M. Bekker - St. Petersburg Math. J. 22 (2011), 883-894
- DOI: https://doi.org/10.1090/S1061-0022-2011-01174-4
- Published electronically: August 18, 2011
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Abstract:
A Schrödinger operator on the axis is considered; its localized potential is the sum of a small potential and certain potentials with contracting supports, which can increase unboundedly when their supports are contracted. Sufficient conditions are presented for the absence (or existence) of eigenvalues for such an operator. In the case where eigenvalues exist, their asymptotic expansion is constructed.References
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Bibliographic Information
- R. R. Gadyl′shin
- Affiliation: Bashkir State Pedagogical University, Ul. Oktyabrskoi Revolyutsii 3a, Ufa 450000, Russia
- Email: gadylshin@yandex.ru
- I. Kh. Khusnullin
- Affiliation: Bashkir State Pedagogical University, Ul. Oktyabrskoi Revolyutsii 3a, Ufa 450000, Russia
- Email: khusnullini@yandex.ru
- Received by editor(s): July 11, 2010
- Published electronically: August 18, 2011
- Additional Notes: Supported by RFBR-Volga region (grant no. 08-01-97016-r), a grant of the President of Russia for support of leading scientific schools (NSh-6249.2010.1) and by FPTs (02.740.110612). The second author was also supported by a grant of the President of Russia for support of young Doctors of Science (MD-453.2010.1)
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 883-894
- MSC (2010): Primary 35J10; Secondary 35P20
- DOI: https://doi.org/10.1090/S1061-0022-2011-01174-4
- MathSciNet review: 2798766
Dedicated: Dedicated to Vasiliĭ Mikhaĭlovich Babich, a remarkable mathematician and personality