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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 2, Pages 195–211 (Mi msb1993)  

This article is cited in 5 scientific papers (total in 5 papers)

A complete asymptotic expansion of the spectral function of second order elliptic operators in $\mathbf R^n$

B. R. Vainberg


Abstract: A complete asymptotic expansion as $\lambda\to\infty$, $|x|,|y|\leqslant b<\infty$ ($b$ arbitrary) is obtained for the spectral function $e_\lambda(x,y)$ of second order elliptic operators in $\mathbf R^n$ satisfying the condition of not being “trapped”, i.e. the requirement that the bicharacteristics issuing from any point extend to infinity.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 191–206

Bibliographic databases:

UDC: 517.95
MSC: Primary 35P05, 47F05, 41A60; Secondary 35J15
Received: 20.04.1983

Citation: B. R. Vainberg, “A complete asymptotic expansion of the spectral function of second order elliptic operators in $\mathbf R^n$”, Mat. Sb. (N.S.), 123(165):2 (1984), 195–211; Math. USSR-Sb., 51:1 (1985), 191–206

Citation in format AMSBIB
\Bibitem{Vai84}
\by B.~R.~Vainberg
\paper A~complete asymptotic expansion of the spectral function of second order elliptic operators in~$\mathbf R^n$
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 2
\pages 195--211
\mathnet{http://mi.mathnet.ru/msb1993}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=732385}
\zmath{https://zbmath.org/?q=an:0573.35070}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 1
\pages 191--206
\crossref{https://doi.org/10.1070/SM1985v051n01ABEH002854}


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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. Vainberg B., “The Paramatrix and Asymptotics of the Spectral-Function of Differential-Operators in Rn”, 282, no. 2, 1985, 265–269  mathscinet  isi
    2. Berard PH., “Spectral Geometry - Direct and Inverse Problems”, Lect. Notes Math., 1207 (1986), R1–&  mathscinet  adsnasa  isi
    3. D Robert, H Tamura, “Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes”, Journal of Functional Analysis, 80:1 (1988), 124  crossref
    4. C. Gerard, A. Martinez, “Semiclassical asymptotics for the spectral function of long-range Schrödinger operators”, Journal of Functional Analysis, 84:1 (1989), 226  crossref
    5. Volovoy A., “Improved 2-Term Asymptotics for the Eigenvalue Distribution Function of an Elliptic Operator on a Compact Manifold”, Commun. Partial Differ. Equ., 15:11 (1990), 1509–1563  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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