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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 6, Pages 1177–1228 (Mi izv1395)  

This article is cited in 8 scientific papers (total in 8 papers)

The method of approximate spectral projection

S. Z. Levendorskii


Abstract: A method is developed for proving a classical formula for the asymptotic behavior of the spectrum in various spectral problems, with a certain estimate of the remainder. Considered as applications are linear pencils both on bounded and on unbounded regions, problems in the theory of shells, and the problem of the asymptotic behavior of a discrete spectrum accumulating to the boundary of the essential spectrum for Schrödinger and Dirac operators.
Bibliography: 74 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 27:3, 451–502

Bibliographic databases:

UDC: 517.956
MSC: Primary 35J10, 35P20, 35S15, 47A10; Secondary 35J10, 73L20
Received: 31.01.1983

Citation: S. Z. Levendorskii, “The method of approximate spectral projection”, Izv. Akad. Nauk SSSR Ser. Mat., 49:6 (1985), 1177–1228; Math. USSR-Izv., 27:3 (1986), 451–502

Citation in format AMSBIB
\Bibitem{Lev85}
\by S.~Z.~Levendorskii
\paper The method of approximate spectral projection
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 6
\pages 1177--1228
\mathnet{http://mi.mathnet.ru/izv1395}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=816853}
\zmath{https://zbmath.org/?q=an:0614.35021}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 27
\issue 3
\pages 451--502
\crossref{https://doi.org/10.1070/IM1986v027n03ABEH001185}


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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. A. S. Andreev, “Asymptotics of the spectrum of compact pseudodifferential operators in a Euclidean domain”, Math. USSR-Sb., 65:1 (1990), 205–228  mathnet  crossref  mathscinet  zmath
    2. S. Z. Levendorskii, “Non-classical spectral asymptotics”, Russian Math. Surveys, 43:1 (1988), 149–192  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. Z. Levendorskii, “On types of degenerate elliptic operators”, Math. USSR-Sb., 66:2 (1990), 523–540  mathnet  crossref  mathscinet  zmath  isi
    4. K. Kh. Boimatov, A. G. Kostyuchenko, “Eigenvalues of the equation $Au=\lambda Bu$ on a compact manifold without boundary”, Funct. Anal. Appl., 23:1 (1989), 52–53  mathnet  crossref  mathscinet  zmath  isi
    5. A. S. Andreev, “Estimates of the spectrum of compact pseudodifferential operators in unbounded domains”, Math. USSR-Sb., 70:2 (1991), 431–443  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. K. Kh. Boimatov, “Asymptotics of spectral projectors of pseudodifferential operators”, Funct. Anal. Appl., 26:1 (1992), 42–44  mathnet  crossref  mathscinet  zmath  isi
    7. V. M. Kaplitskiǐ, “Asymptotics of the distribution of eigenvalues of a selfadjoint second order hyperbolic differential operator on the two-dimensional torus”, Siberian Math. J., 51:5 (2010), 830–846  mathnet  crossref  mathscinet  isi  elib
    8. V. I. Bezyaev, “Ob asimptotike plotnosti sostoyanii gipoellipticheskikh pochti-periodicheskikh sistem”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 593–604  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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