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Mat. Sb., 1993, Volume 184, Number 6, Pages 83–98 (Mi msb994)  

This article is cited in 1 scientific paper (total in 1 paper)

Spectrum and completeness of natural oscillations of the atmosphere with temperature stratification

S. A. Stepin

M. V. Lomonosov Moscow State University

Abstract: Study of the vertical structure of small oscillations of the atmosphere leads to a nonselfadjoint singular boundary eigenvalue problem containing the spectral parameter in the equation and the boundary condition. In this article the problem in question is reduced to the spectral analysis of the operator pencil $\mathcal L(\lambda)=I-\lambda U-(1/\lambda)V$, where $U$ and $V$ are positive compact operators in $L_2(0,\infty)$. By means of a technique based on the study of the energy quadratic form and application of the theory of operator pencils it is proved that the eigenvalues of the problem are real, and their multiplicity is computed; existence of two Riesz bases composed of eigenfunctions is established, and the property of twofold completeness of the system of eigenfunctions and associated functions in the Hilbert space corresponding to the physical formulation of the problem is proved.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:1, 179–190

Bibliographic databases:

UDC: 517.9
MSC: Primary 76C15, 86A10, 34L10; Secondary 47A56
Received: 08.04.1992

Citation: S. A. Stepin, “Spectrum and completeness of natural oscillations of the atmosphere with temperature stratification”, Mat. Sb., 184:6 (1993), 83–98; Russian Acad. Sci. Sb. Math., 79:1 (1994), 179–190

Citation in format AMSBIB
\Bibitem{Ste93}
\by S.~A.~Stepin
\paper Spectrum and completeness of natural oscillations of the~atmosphere with temperature stratification
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 6
\pages 83--98
\mathnet{http://mi.mathnet.ru/msb994}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1234591}
\zmath{https://zbmath.org/?q=an:0816.76023}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 79
\issue 1
\pages 179--190
\crossref{https://doi.org/10.1070/SM1994v079n01ABEH003496}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PP19200012}


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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. S. A. Stepin, “On the resonance effect for singularly perturbed operator bundles”, Russian Math. Surveys, 51:5 (1996), 1003–1005  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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