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Mat. Sb. (N.S.), 1984, Volume 124(166), Number 2(6), Pages 251–271 (Mi msb2050)  

This article is cited in 5 scientific papers (total in 5 papers)

Asymptotics of the spectrum of linear operator pencils

S. Z. Levendorskii


Abstract: The problem $Au=tBu$ is considered in a bounded Lipschitz domain, where $A$ and are sums of a pseudodifferential operator satisfying a transmission condition and a singular Green operator, with $A$ elliptic. Under natural conditions the classical formula for the asymptotics of the spectrum is established, with an estimate of the remainder determined by the character of degeneration in ellipticity of the operator $B$.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 52:1, 245–266

Bibliographic databases:

UDC: 517.956
MSC: Primary 35P20, 47G05; Secondary 35S99, 47A10, 58B20
Received: 21.12.1981 and 25.01.1983

Citation: S. Z. Levendorskii, “Asymptotics of the spectrum of linear operator pencils”, Mat. Sb. (N.S.), 124(166):2(6) (1984), 251–271; Math. USSR-Sb., 52:1 (1985), 245–266

Citation in format AMSBIB
\Bibitem{Lev84}
\by S.~Z.~Levendorskii
\paper Asymptotics of the spectrum of linear operator pencils
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 124(166)
\issue 2(6)
\pages 251--271
\mathnet{http://mi.mathnet.ru/msb2050}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=746070}
\zmath{https://zbmath.org/?q=an:0571.35081|0553.35067}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 52
\issue 1
\pages 245--266
\crossref{https://doi.org/10.1070/SM1985v052n01ABEH002887}


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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. S. Z. Levendorskii, “The method of approximate spectral projection”, Math. USSR-Izv., 27:3 (1986), 451–502  mathnet  crossref  mathscinet  zmath
    2. S. Z. Levendorskii, “Asymptotics of the spectrum of problems with constraints”, Math. USSR-Sb., 57:1 (1987), 77–95  mathnet  crossref  mathscinet  zmath
    3. Levendorskii S., “The Approximate Spectral Projection Method”, Acta Appl. Math., 7:2 (1986), 137–197  crossref  mathscinet  isi
    4. K. Kh. Boimatov, “Asymptotics of spectral projectors of pseudodifferential operators”, Funct. Anal. Appl., 26:1 (1992), 42–44  mathnet  crossref  mathscinet  zmath  isi
    5. Mark S. Ashbaugh, Fritz Gesztesy, Marius Mitrea, Gerald Teschl, “Spectral theory for perturbed Krein Laplacians in nonsmooth domains”, Advances in Mathematics, 223:4 (2010), 1372  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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