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

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

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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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
2. Berard PH., “Spectral Geometry - Direct and Inverse Problems”, Lect. Notes Math., 1207 (1986), R1–&
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
4. C. Gerard, A. Martinez, “Semiclassical asymptotics for the spectral function of long-range Schrödinger operators”, Journal of Functional Analysis, 84:1 (1989), 226
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
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