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Mathematics of the USSR-Sbornik, 1981, Volume 38, Issue 1, Pages 61–81
DOI: https://doi.org/10.1070/SM1981v038n01ABEH001219 (Mi sm2423) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type

V. I. Feigin
English version PDF (1055 kB) Citations (3)
References:
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DOI: https://doi.org/10.1070/SM1981v038n01ABEH001219
Abstract: Selfadjoint operators $P(x,D)$ in $R^n$, depending on a small parameter $h$ are considered. Asymptotic formulas are established for the number of eigenvalues not exceeding $Mh^R$, where $M$ is a sufficiently large number. $R\leqslant R_0$, and $R_0$ is determined by $P$. In particular, for $R=R_0$ an asymptotic formula is obtained which is analogous to the well-known Bohr–Sommerfeld formula for ordinary differential operators.
Bibliography: 11 titles.
Received: 20.07.1978
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1979, Volume 110(152), Number 1(9), Pages 66–87
Bibliographic databases:
UDC: 517.43
MSC: Primary 35J30, 47F05, 35P20; Secondary 35S05
Language: English
Original paper language: Russian
Citation: V. I. Feigin, “The asymptotic distribution of eigenvalues and a formula of Bohr–Sommerfeld type”, Mat. Sb. (N.S.), 110(152):1(9) (1979), 66–87; Math. USSR-Sb., 38:1 (1981), 61–81
Citation in format AMSBIB
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\by V.~I.~Feigin
\paper The asymptotic distribution of eigenvalues and a~formula of Bohr--Sommerfeld type
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 1(9)
\pages 66--87
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=548517}
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\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 1
\pages 61--81
\crossref{https://doi.org/10.1070/SM1981v038n01ABEH001219}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981LB83400005}
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  • https://www.mathnet.ru/eng/sm/v152/i1/p66
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:331
    Russian version PDF:95
    English version PDF:5
    References:39
     
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