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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 7, Pages 3–13 (Mi ivm9253)  

Perturbation of Hill operator by narrow potentials

A. R. Bikmetova, I. Kh. Khusnullinb

a Ufa Scientific Center of Russian Academy of Sciences, 71 Oktyabrya Ave., Ufa, 450054 Russia
b M. Akmulla Bashkir State Pedagogical University, 3a Oktyabrskoi Revolutsii str., Ufa, 450000 Russia

Abstract: We consider a perturbation of periodic operator of the second order on the axis, which is a special case of the Hill operator. Perturbation is realized by a complex sum of two complex-valued potentials with compact supports depending on two small parameters, one of which describes the length of the carriers of potentials and the reciprocal of the second one corresponds to the maximum values of potential modules. We obtain the sufficient condition, under which from the edges of non-degenerate lacunas of continuous spectrum their eigenvalues arise, and construct asymptotics. We adduce a sufficient condition under which the eigenvalues do not arise.

Keywords: Hill operator, perturbation, asymptotics.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-97024_p_поволжье_a
Ministry of Education and Science of the Russian Federation
Грант Республики Башкортостан молодым ученым и молодежным научным коллективам 4


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:7, 1–10

Bibliographic databases:

UDC: 517.928
Received: 11.03.2016

Citation: A. R. Bikmetov, I. Kh. Khusnullin, “Perturbation of Hill operator by narrow potentials”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 7, 3–13; Russian Math. (Iz. VUZ), 61:7 (2017), 1–10

Citation in format AMSBIB
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\by A.~R.~Bikmetov, I.~Kh.~Khusnullin
\paper Perturbation of Hill operator by narrow potentials
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 7
\pages 3--13
\mathnet{http://mi.mathnet.ru/ivm9253}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 7
\pages 1--10
\crossref{https://doi.org/10.3103/S1066369X17070015}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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