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Trudy Moskovskogo Matematicheskogo Obshchestva, 2019, Volume 80, Issue 2, Pages 179–195 (Mi mmo630)  
Spectral properties of differential operators with oscillating coefficients

N. F. Valeeva, Ya. T. Sultanaevb, É. A. Nazirovab

a Institute of Mathematics with Computer Centre of the Ufa Science Center of the Russian Academy of Science, Ufa, Russia
b Akmulla Bashkir State Pedagogical University, Ufa, Russia
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Abstract: We study the properties of singular Sturm-Liouville operators in Hilbert spaces. Although the literature on the topic is immense, there are a number of questions that have yet to be solved, for example, those pertaining to the behavior of solutions of the Sturm-Liouville equation with an irregular potential at infinity. This problem is topical not only for being of interest in itself but also because it naturally arises when dealing with questions related to the spectral properties of the Sturm-Liouville operator.
Key words and phrases: Sturm–Liouville operator, singular potential, asymptotics of the fundamental solution system.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00250_а
Supported by the Russian Foundation for Basic Research (project No. 18-01-00250).
Received: 27.04.2019
English version:
Transactions of the Moscow Mathematical Society, 2019, Volume 80, Pages 153–167
DOI: https://doi.org/10.1090/mosc/299
Bibliographic databases:
Document Type: Article
UDC: 517.984
MSC: 34L20, 47B38, 47E05
Language: Russian
Citation: N. F. Valeev, Ya. T. Sultanaev, É. A. Nazirova, “Spectral properties of differential operators with oscillating coefficients”, Tr. Mosk. Mat. Obs., 80, no. 2, MCCME, M., 2019, 179–195; Trans. Moscow Math. Soc., 80 (2019), 153–167
Citation in format AMSBIB
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\by N.~F.~Valeev, Ya.~T.~Sultanaev, \'E.~A.~Nazirova
\paper Spectral properties of differential operators with oscillating coefficients
\serial Tr. Mosk. Mat. Obs.
\yr 2019
\vol 80
\issue 2
\pages 179--195
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo630}
\elib{https://elibrary.ru/item.asp?id=43264314}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 153--167
\crossref{https://doi.org/10.1090/mosc/299}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083793557}
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