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Contemporary Mathematics. Fundamental Directions, 2017, Volume 63, Issue 3, Pages 373–391
DOI: https://doi.org/10.22363/2413-3639-2017-63-3-373-391
(Mi cmfd325)
 

This article is cited in 3 scientific papers (total in 3 papers)

On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip

D. I. Borisovabc

a Institute of Mathematics with Computer Center, Ufa Science Center, Russian Academy of Sciences, 112 Chernyshevskogo st., 450008 Ufa, Russia
b Bashkir State Pedagogical University, 3a Oktyabr'skoy Revolutsii st., 450000 Ufa, Russia
c University of Hradec Králové, 62 Rokitanského st., 500 03 Hradec Králové, Czech Republic
Full-text PDF (224 kB) Citations (3)
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Abstract: We consider the Schrödinger periodic magnetic operator in an infinite flat straight strip. We prove that if the magnetic potential satisfies certain conditions and the period is small enough, then the lower part of the band spectrum has no inner lacunas. The length of the lower part of the band spectrum with no inner lacunas is calculated explicitly. The upper estimate for the small parameter allowing these results is calculated as a number as well.
Funding agency Grant number
Russian Science Foundation 17-11-01004
Document Type: Article
UDC: 517.958+517.984+519.21
Language: Russian
Citation: D. I. Borisov, “On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 373–391
Citation in format AMSBIB
\Bibitem{Bor17}
\by D.~I.~Borisov
\paper On lacunas in the lower part of the spectrum of the periodic magnetic operator in a~strip
\inbook Differential and functional differential equations
\serial CMFD
\yr 2017
\vol 63
\issue 3
\pages 373--391
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd325}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-3-373-391}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Современная математика. Фундаментальные направления
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    References:31
     
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