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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 4(12), Pages 571–588 (Mi msb3494)  

This article is cited in 35 scientific papers (total in 35 papers)

On asymptotic distribution of eigenvalues of pseudodifferential operators in $\mathbf R^n$

V. N. Tulovskii, M. A. Shubin


Abstract: This paper is devoted to the study of asymptotic behavior of eigenvalues of a pseudodifferential operator in $\mathbf R^n$. With certain conditions imposed on the symbol of the operator, the asymptotics of the eigenvalues, with remainder, is obtained.
Bibliography: 10 titles.

Full text: PDF file (1225 kB)
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English version:
Mathematics of the USSR-Sbornik, 1973, 21:4, 565–583

Bibliographic databases:

UDC: 517.43
MSC: 35P20, 35S99, 47G05
Received: 06.03.1973

Citation: V. N. Tulovskii, M. A. Shubin, “On asymptotic distribution of eigenvalues of pseudodifferential operators in $\mathbf R^n$”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 571–588; Math. USSR-Sb., 21:4 (1973), 565–583

Citation in format AMSBIB
\Bibitem{TulShu73}
\by V.~N.~Tulovskii, M.~A.~Shubin
\paper On~asymptotic distribution of eigenvalues of pseudodifferential operators in~$\mathbf R^n$
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 4(12)
\pages 571--588
\mathnet{http://mi.mathnet.ru/msb3494}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=331131}
\zmath{https://zbmath.org/?q=an:0286.35059}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 4
\pages 565--583
\crossref{https://doi.org/10.1070/SM1973v021n04ABEH002036}


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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. M. A. Shubin, “Almost-periodic elliptic operators and von Neumann algebras”, Funct. Anal. Appl., 9:1 (1975), 88–89  mathnet  crossref  mathscinet  zmath
    2. V. I. Feigin, “Asymptotic distribution of eigenvalues for hypoelliptic systems in $R^n$”, Math. USSR-Sb., 28:4 (1976), 533–552  mathnet  crossref  mathscinet  zmath  isi
    3. V. I. Feigin, “Dve algebry psevdodifferentsialnykh operatorov v $R^n$ i nekotorye prilozheniya”, UMN, 31:2(188) (1976), 233–234  mathnet  mathscinet  zmath
    4. V. L. Roitburd, “O kvaziklassicheskoi asimptotike spektra psevdo differentsialnogo operatora”, UMN, 31:4(190) (1976), 275–276  mathnet  mathscinet  zmath
    5. B. V. Fedosov, “A periodicity theorem in the algebra of symbols”, Math. USSR-Sb., 34:3 (1978), 382–410  mathnet  crossref  mathscinet  zmath
    6. V. I. Bezyaev, “Asymptotics of the density of states of hypoelliptic almost periodic operators”, Math. USSR-Sb., 34:4 (1978), 425–447  mathnet  crossref  mathscinet  zmath
    7. D. Robert, “Proprietes spectrales d'operators pseduo-differentiels”, Communications in Partial Differential Equations, 3:9 (1978), 755  crossref
    8. M. A. Shubin, “The spectral theory and the index of elliptic operators with almost periodic coefficients”, Russian Math. Surveys, 34:2 (1979), 109–157  mathnet  crossref  mathscinet  zmath
    9. S. Z. Levendorskii, “General calculus of pseudodifferential operators and asymptotic properties of the spectrum”, Funct. Anal. Appl., 15:2 (1981), 140–142  mathnet  crossref  mathscinet  zmath  isi
    10. V Guillemin, S Sternberg, “The metaplectic representation, Weyl operators and spectral theory”, Journal of Functional Analysis, 42:2 (1981), 128  crossref
    11. Levendorskii S., “Quasi-Classical Asymptotics of Eigenvalues of Systems of Pseudodifferential-Operators”, 256, no. 1, 1981, 32–36  isi
    12. V. I. Bezyaev, “Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold”, Math. USSR-Sb., 45:2 (1983), 169–189  mathnet  crossref  mathscinet  zmath
    13. S. Z. Levendorskii, “Asymptotic distribution of eigenvalues”, Math. USSR-Izv., 21:1 (1983), 119–160  mathnet  crossref  mathscinet  zmath
    14. V. I. Feigin, “Sharp estimates of the remainder in the spectral asymptotic for pseudodifferential operators in $\mathbb{R}^n$”, Funct. Anal. Appl., 16:3 (1982), 233–235  mathnet  crossref  mathscinet  zmath  isi
    15. Levendorskii S., “On a General-Method of Investigation of the Spectral Asymptotics and its Application to the Theory of Shells”, 266, no. 2, 1982, 276–280  isi
    16. S. Z. Levendorskii, “Distribution of eigenvalues of systems of the form $Au=tBu$”, Funct. Anal. Appl., 17:2 (1983), 149–151  mathnet  crossref  mathscinet  zmath  isi
    17. B Helffer, D Robert, “Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles”, Journal of Functional Analysis, 53:3 (1983), 246  crossref
    18. Didier Robert, “Remarks on a paper of S. Zelditch: “Szegö limit theorems in quantum mechanics””, Journal of Functional Analysis, 53:3 (1983), 304  crossref
    19. Levendorskii S., “The Approximate Spectral Projector Method as a General-Method of the Grounding of the Spectral Asymptotics Classical Formula”, 271, no. 2, 1983, 287–291  isi
    20. S. Z. Levendorskii, “Asymptotics of the spectrum of linear operator pencils”, Math. USSR-Sb., 52:1 (1985), 245–266  mathnet  crossref  mathscinet  zmath
    21. S. Z. Levendorskii, “Asymptotic distribution of the eigenvalues of systems of Navier–Stokes type”, Russian Math. Surveys, 39:4 (1984), 129–130  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. S. Z. Levendorskii, “Asymptotic behavior of the spectrum of problems of the form $Au=tBu$ for operators that are elliptic in the Douglis–Nirenberg sense”, Funct. Anal. Appl., 18:3 (1984), 253–255  mathnet  crossref  mathscinet  zmath  isi
    23. Levendorskii S., “Spectral Asymptotics for Problems with Connections”, 276, no. 2, 1984, 282–285  isi
    24. Ivrii V., “Precise Spectral Asymptotics for Elliptic-Operators Acting in Fiberlings Over Manifolds with Boundary - Introduction”, 1100, 1984, R4–238  isi
    25. S. Z. Levendorskii, “The method of approximate spectral projection”, Math. USSR-Izv., 27:3 (1986), 451–502  mathnet  crossref  mathscinet  zmath
    26. Victor Guillemin, “A new proof of Weyl's formula on the asymptotic distribution of eigenvalues”, Advances in Mathematics, 55:2 (1985), 131  crossref
    27. S. Z. Levendorskii, “Asymptotics of the spectrum of problems with constraints”, Math. USSR-Sb., 57:1 (1987), 77–95  mathnet  crossref  mathscinet  zmath
    28. Levendorskii S., “The Approximate Spectral Projection Method”, Acta Appl. Math., 7:2 (1986), 137–197  crossref  isi
    29. S. Z. Levendorskii, “Non-classical spectral asymptotics”, Russian Math. Surveys, 43:1 (1988), 149–192  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    30. S. I. Boyarchenko, S. Z. Levendorskii, “Spectral Asymptotics of Laplacians on Horns: the Case of a Rapidly Growing Counting Function”, Funct. Anal. Appl., 32:3 (1998), 198–200  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. Lech Zielinski, “Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators”, Math Phys Anal Geom, 9:1 (2006), 1  crossref  mathscinet  isi  elib
    32. Ernesto Buzano, “Analytic semigroups generated by globally hypoelliptic operators”, Integral Transforms and Special Functions, 17:2-3 (2006), 157  crossref
    33. Lech Zielinski, “Sharp semiclassical estimates for the number of eigenvalues below a totally degenerate critical level”, Journal of Functional Analysis, 248:2 (2007), 259  crossref
    34. Ernesto Buzano, Fabio Nicola, “Complex powers of hypoelliptic pseudodifferential operators”, Journal of Functional Analysis, 245:2 (2007), 353  crossref
    35. Ernesto Buzano, Andrea Ziggioto, “On the essential spectrum of hypoelliptic pseudo-differential operators”, Math Nachr, 281:1 (2008), 5  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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