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Izvestiya: Mathematics, 2008, Volume 72, Issue 4, Pages 659–688
DOI: https://doi.org/10.1070/IM2008v072n04ABEH002420
(Mi im1146)
 

This article is cited in 26 scientific papers (total in 26 papers)

On the spectrum of a periodic operator with a small localized perturbation

D. I. Borisov, R. R. Gadyl'shin

Bashkir State Pedagogical University
References:
Abstract: The paper deals with the spectrum of a periodic self-adjoint differential operator on the real axis perturbed by a small localized non-self-adjoint operator. We show that the continuous spectrum does not depend on the perturbation, the residual spectrum is empty, and the point spectrum has no finite accumulation points. We study the problem of the existence of eigenvalues embedded in the continuous spectrum, obtain necessary and sufficient conditions for the existence of eigenvalues, construct asymptotic expansions of the eigenvalues and corresponding eigenfunctions and consider some examples.
Received: 25.08.2006
Revised: 24.03.2008
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2008, Volume 72, Issue 4, Pages 37–66
DOI: https://doi.org/10.4213/im1146
Bibliographic databases:
UDC: 517.984
Language: English
Original paper language: Russian
Citation: D. I. Borisov, R. R. Gadyl'shin, “On the spectrum of a periodic operator with a small localized perturbation”, Izv. RAN. Ser. Mat., 72:4 (2008), 37–66; Izv. Math., 72:4 (2008), 659–688
Citation in format AMSBIB
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\paper On the spectrum of a~periodic operator with a~small localized perturbation
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  • https://www.mathnet.ru/eng/im1146
  • https://doi.org/10.1070/IM2008v072n04ABEH002420
  • https://www.mathnet.ru/eng/im/v72/i4/p37
  • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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