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 Mat. Sb. (N.S.), 1982, Volume 117(159), Number 2, Pages 161–180 (Mi msb2197)

Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold

V. I. Bezyaev

Abstract: In this article an asymptotic formula with an estimate of the remainder term is proved for the distribution function of the eigenvalues of hypoelliptic differential operators on a compact manifold without boundary. The proof is based on a method for constructing an approximate spectral projection for the operators under consideration.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 45:2, 169–189

Bibliographic databases:

UDC: 517.43
MSC: 35H05, 35P20

Citation: V. I. Bezyaev, “Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold”, Mat. Sb. (N.S.), 117(159):2 (1982), 161–180; Math. USSR-Sb., 45:2 (1983), 169–189

Citation in format AMSBIB
\Bibitem{Bez82} \by V.~I.~Bezyaev \paper Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold \jour Mat. Sb. (N.S.) \yr 1982 \vol 117(159) \issue 2 \pages 161--180 \mathnet{http://mi.mathnet.ru/msb2197} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=644767} \zmath{https://zbmath.org/?q=an:0512.35067|0485.35073} \transl \jour Math. USSR-Sb. \yr 1983 \vol 45 \issue 2 \pages 169--189 \crossref{https://doi.org/10.1070/SM1983v045n02ABEH001002} 

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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, “Asymptotics of the spectrum of linear operator pencils”, Math. USSR-Sb., 52:1 (1985), 245–266
2. S. Z. Levendorskii, “The method of approximate spectral projection”, Math. USSR-Izv., 27:3 (1986), 451–502
3. S. Z. Levendorskii, “Non-classical spectral asymptotics”, Russian Math. Surveys, 43:1 (1988), 149–192
4. Zielinski L., “Asymptotic-Behavior of Eigenvalues of Differential-Operators with Nonregular Coefficients on a Compact Manifold”, Comptes Rendus Acad. Sci. Ser. I-Math., 310:7 (1990), 563–568
5. 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
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