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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 437–465 (Mi izv2256)  

This article is cited in 6 scientific papers (total in 6 papers)

Asymptotics of the eigenvalues of the Laplacian and quasimodes. A series of quasimodes corresponding to a system of caustics close to the boundary of the domain

V. F. Lazutkin


Abstract: For a bounded convex domain in the plane, asymptotic formulas with error tending to zero are constructed for a certain series of eigenvalues of the Laplacian with zero boundary conditions. The boundary of the domain is assumed to be sufficiently smooth. It is proved that
$$ \varliminf_{\lambda\to+\infty}N^*(\lambda)/N(\lambda)>0, $$
where $N(\lambda)$ is the number of eigenvalues (with multiplicities taken into account) less than $\lambda$ and $N^*(\lambda)$ is the number of those eigenvalues for which an asymptotic expansion has been found.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 439–466

Bibliographic databases:

UDC: 517.43
MSC: 35P20, 35J05, 47F05
Received: 07.02.1972

Citation: V. F. Lazutkin, “Asymptotics of the eigenvalues of the Laplacian and quasimodes. A series of quasimodes corresponding to a system of caustics close to the boundary of the domain”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 437–465; Math. USSR-Izv., 7:2 (1973), 439–466

Citation in format AMSBIB
\Bibitem{Laz73}
\by V.~F.~Lazutkin
\paper Asymptotics of the eigenvalues of the Laplacian and quasimodes. A~series of quasimodes corresponding to a~system of caustics close to the boundary of the domain
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 437--465
\mathnet{http://mi.mathnet.ru/izv2256}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=333485}
\zmath{https://zbmath.org/?q=an:0255.35074}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 439--466
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001949}


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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. I. Shnirelman, “Ob asimptoticheskoi kratkosti spektra operatora Laplasa”, UMN, 30:4(184) (1975), 265–266  mathnet  mathscinet  zmath
    2. M V Berry, J Phys A Math Gen, 10:12 (1977), 2083  crossref  zmath  adsnasa
    3. Vadim Zharnitsky, “Quasiperiodic Motion in the Billiard Problem with a Softened Boundary”, Phys. Rev. Lett, 75:24 (1995), 4393  crossref
    4. P. Stefanov, G. Vodev, “Neumann resonances in linear elasticity for an arbitrary body”, Comm Math Phys, 176:3 (1996), 645  crossref  mathscinet  zmath  adsnasa
    5. Martin Kunz, J Phys A Math Gen, 33:31 (2000), 5567  crossref  mathscinet  zmath
    6. J. Math. Sci. (N. Y.), 128:2 (2005), 2680–2685  mathnet  crossref  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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