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Mat. Sb. (N.S.), 1986, Volume 130(172), Number 2(6), Pages 243–264 (Mi msb1867)  

This article is cited in 4 scientific papers (total in 4 papers)

Parametrix and asymptotics of the spectral function of differential operators in $\mathbf R^n$

B. R. Vainberg


Abstract: A new formula is obtained for a global parametrix of the Cauchy problem for hyperbolic equations and systems which is an analogue of the representation of the Green function in terms of the spectral function of the corresponding steady-state operator. In the selfadjoint case this formula makes it possible to obtain a complete asymptotic expansion of the spectral function of elliptic operators in $\mathbf R^n$.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 58:1, 245–265

Bibliographic databases:

UDC: 517.95
MSC: Primary 35L15; Secondary 35P99
Received: 25.01.1984 and 17.09.1984

Citation: B. R. Vainberg, “Parametrix and asymptotics of the spectral function of differential operators in $\mathbf R^n$”, Mat. Sb. (N.S.), 130(172):2(6) (1986), 243–264; Math. USSR-Sb., 58:1 (1987), 245–265

Citation in format AMSBIB
\Bibitem{Vai86}
\by B.~R.~Vainberg
\paper Parametrix and asymptotics of the spectral function of differential operators in~$\mathbf R^n$
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 2(6)
\pages 243--264
\mathnet{http://mi.mathnet.ru/msb1867}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854974}
\zmath{https://zbmath.org/?q=an:0658.47048|0622.47051}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 1
\pages 245--265
\crossref{https://doi.org/10.1070/SM1987v058n01ABEH003102}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. G. Safarov, “Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition”, Funct. Anal. Appl., 22:3 (1988), 213–223  mathnet  crossref  mathscinet  zmath  isi
    2. Efremov D., “Spectral-Function Asymptotics for 2nd Order Elliptic-Operators on Lobachevsky Spaces”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1988, no. 3, 73–75  mathscinet  zmath  isi
    3. 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
    4. A. I. Kozko, A. S. Pechentsov, “The spectral function of a singular differential operator of order $2m$”, Izv. Math., 74:6 (2010), 1205–1224  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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