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Mat. Zametki, 1973, Volume 14, Issue 3, Pages 361–368 (Mi mz7265)  

This article is cited in 1 scientific paper (total in 1 paper)

On the formula for the distribution of the eigenvalues of singular differential operators

M. Otelbaev, Ya. T. Sultanaev

M. V. Lomonosov Moscow State University

Abstract: In this note we construct exampLes of a function $q(x)$, which grows arbitrarily rapidly, and a function $q(x)$ ($c_1|x|^\alpha\le q(x)\le c_2|x|^\beta$, $\beta>\alpha>0$) such that for a Sturm–Liouville operator with the constructed potential functions $q(x)$, the classical formula for the number of eigenvalues of the operator that do not exceed $\lambda$ is not true.

Full text: PDF file (386 kB)

English version:
Mathematical Notes, 1973, 14:3, 768–771

Bibliographic databases:

UDC: 513.88
Received: 01.12.1972

Citation: M. Otelbaev, Ya. T. Sultanaev, “On the formula for the distribution of the eigenvalues of singular differential operators”, Mat. Zametki, 14:3 (1973), 361–368; Math. Notes, 14:3 (1973), 768–771

Citation in format AMSBIB
\Bibitem{OteSul73}
\by M.~Otelbaev, Ya.~T.~Sultanaev
\paper On the formula for the distribution of the eigenvalues of singular differential operators
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 3
\pages 361--368
\mathnet{http://mi.mathnet.ru/mz7265}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=343101}
\zmath{https://zbmath.org/?q=an:0306.34029}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 3
\pages 768--771
\crossref{https://doi.org/10.1007/BF01147452}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. Kh. Boimatov, “Asimptotika spektra operatora Shredingera s singulyarnym potentsialom”, UMN, 31:1(187) (1976), 241–242  mathnet  mathscinet  zmath
  • Математические заметки Mathematical Notes
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