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Mat. Sb. (N.S.), 1987, Volume 133(175), Number 3(7), Pages 293–313 (Mi msb2563)  

This article is cited in 11 scientific papers (total in 11 papers)

On the basis property for a certain part of the eigenvectors and associated vectors of a selfadjoint operator pencil

A. S. Markus, V. I. Matsaev


Abstract: Let $L(\lambda)=A+\lambda I+\lambda^2B$ be a quadratic pencil, where $A$ and $B$ are compact selfadjoint operators on a separable Hilbert space $\mathfrak H$. Two subsystems of eigenvectors and associated vectors are constructed for the pencil $L(\lambda)$, each of them forming a Riesz basis for $\mathfrak H$.
Bibliography: 24 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 61:2, 289–307

Bibliographic databases:

UDC: 517.984
MSC: Primary 47A56, 47A70; Secondary 47A10, 47B10, 47B15
Received: 09.04.1986

Citation: A. S. Markus, V. I. Matsaev, “On the basis property for a certain part of the eigenvectors and associated vectors of a selfadjoint operator pencil”, Mat. Sb. (N.S.), 133(175):3(7) (1987), 293–313; Math. USSR-Sb., 61:2 (1988), 289–307

Citation in format AMSBIB
\Bibitem{MarMat87}
\by A.~S.~Markus, V.~I.~Matsaev
\paper On the basis property for a~certain part of the eigenvectors and associated vectors of a~selfadjoint operator pencil
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 133(175)
\issue 3(7)
\pages 293--313
\mathnet{http://mi.mathnet.ru/msb2563}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=909853}
\zmath{https://zbmath.org/?q=an:0677.47008|0632.47015}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 61
\issue 2
\pages 289--307
\crossref{https://doi.org/10.1070/SM1988v061n02ABEH003208}


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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. Miloslavskii A., “Small Oscillations Spectrum of Hereditary Viscoelastic Solid”, 309, no. 3, 1989, 532–536  mathscinet  isi
    2. S. A. Stepin, “Spectrum and completeness of natural oscillations of the atmosphere with temperature stratification”, Russian Acad. Sci. Sb. Math., 79:1 (1994), 179–190  mathnet  crossref  mathscinet  zmath  isi
    3. Roman I. Andrushkiw, “On the Spectral Theory of Operator Pencils in a Hilbert Space”, Journal of Nonlinear Mathematical Physics, 2:3-4 (1995), 356  crossref
    4. Reinhard Mennicken, Andrey A. Shkalikov, “Spectral Decomposition of Symmetric Operator Matrices”, Math Nachr, 179:1 (1996), 259  crossref  mathscinet  zmath  isi
    5. R. Mennicken, A. K. Motovilov, “Operator interpretation of the resonances generated by 2×2 matrix Hamiltonians”, Theor Math Phys, 116:2 (1998), 867  mathnet  crossref  mathscinet  zmath  isi  elib
    6. Reinhard Mennicken, Alexander K. Motovilov, “Operator Interpretation of Resonances Arising in Spectral Problems for 2 × 2 Operator Matrices”, Math Nachr, 201:1 (1999), 117  crossref  elib
    7. H. Langer, A. Markus, V. Matsaev, C. Tretter, “Self-adjoint block operator matrices with non-separated diagonal entries and their Schur complements”, Journal of Functional Analysis, 199:2 (2003), 427  crossref
    8. H. Langer, A. Markus, V. Matsaev, “Self-adjoint analytic operator functions and their local spectral function”, Journal of Functional Analysis, 235:1 (2006), 193  crossref
    9. V. I. Voititskiy, N. D. Kopachevskiy, P. A. Starkov, “Multicomponent conjugation problems and auxiliary abstract boundary-value problems”, Journal of Mathematical Sciences, 170:2 (2010), 131–172  mathnet  crossref  mathscinet
    10. E. A. Larionov, E. M. Zveryaev, T. S. Aleroev, “K teorii slabogo vozmuscheniya normalnykh operatorov”, Preprinty IPM im. M. V. Keldysha, 2014, 014, 31 pp.  mathnet
    11. K. A. Radomirskaya, “Spektralnye i nachalno-kraevye zadachi sopryazheniya”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 63, no. 2, Rossiiskii universitet druzhby narodov, M., 2017, 316–339  mathnet  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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