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.
\Bibitem{Bez82}
\by V.~I.~Bezyaev
\paper Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 2
\pages 169--189
\mathnet{http://mi.mathnet.ru/eng/sm2197}
\crossref{https://doi.org/10.1070/SM1983v045n02ABEH001002}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=644767}
\zmath{https://zbmath.org/?q=an:0512.35067|0485.35073}
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https://www.mathnet.ru/eng/sm2197
https://doi.org/10.1070/SM1983v045n02ABEH001002
https://www.mathnet.ru/eng/sm/v159/i2/p161
This publication is cited in the following 5 articles:
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
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
S. Z. Levendorskii, “Non-classical spectral asymptotics”, Russian Math. Surveys, 43:1 (1988), 149–192
S. Z. Levendorskii, “The method of approximate spectral projection”, Math. USSR-Izv., 27:3 (1986), 451–502
S. Z. Levendorskii, “Asymptotics of the spectrum of linear operator pencils”, Math. USSR-Sb., 52:1 (1985), 245–266
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