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Schrödinger operator on the axis with potentials depending on two parameters


Authors: R. R. Gadyl′shin and I. Kh. Khusnullin
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 22 (2010), nomer 6.
Journal: St. Petersburg Math. J. 22 (2011), 883-894
MSC (2010): Primary 35J10; Secondary 35P20
Published electronically: August 18, 2011
MathSciNet review: 2798766
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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

DOI: https://doi.org/10.1090/S1061-0022-2011-01174-4
Keywords: Schrödinger operator, perturbation
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)
Dedicated: Dedicated to Vasiliĭ Mikhaĭlovich Babich, a remarkable mathematician and personality
Article copyright: © Copyright 2011 American Mathematical Society