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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2009, Volume 9, Issue 1, Pages 31–44 (Mi isu30)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

On properties of the eigenfunctions of a quadratic pencil of the second order differential operators

V. S. Rykhlov

Saratov State University named after N. G. Chernyshevsky

Abstract: The degenerated second order ordinary differential quadratic pencil with constant coefficients is considered. The case is studied, when the roots of characteristic equation lie on a straight line coming through the origin and on the both side of the origin. Properties of the system of its eigenfunctions in the spaces $L_2[0,\sigma]$, $\sigma>0$ is investigated. Criteria of one-fold completeness and minimality of this systemare proved and sufficient conditions of one-fold completeness and minimality are found.

Key words: ordinary differential pencil of operators, quadratic pencil of operators, degenerated pencil of operators, second order, constant coefficients, eigenfunctions, one-fold completeness, onefold minimality, sufficient conditions.

DOI: https://doi.org/10.18500/1816-9791-2009-9-1-31-44

Full text: PDF file (270 kB)
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UDC: 517.927.25

Citation: V. S. Rykhlov, “On properties of the eigenfunctions of a quadratic pencil of the second order differential operators”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 9:1 (2009), 31–44

Citation in format AMSBIB
\Bibitem{Ryk09}
\by V.~S.~Rykhlov
\paper On properties of the eigenfunctions of a~quadratic pencil of the second order differential operators
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 1
\pages 31--44
\mathnet{http://mi.mathnet.ru/isu30}
\crossref{https://doi.org/10.18500/1816-9791-2009-9-1-31-44}


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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. V. S. Rykhlov, O. V. Parfilova, “O kratnoi polnote kornevykh funktsii puchkov differentsialnykh operatorov s postoyannymi koeffitsientami”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:4 (2011), 45–58  mathnet  crossref
    2. V. S. Rykhlov, “O kratnoi polnote kornevykh funktsii obyknovennogo differentsialnogo polinomialnogo puchka s postoyannymi koeffitsientami”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 63, no. 2, Rossiiskii universitet druzhby narodov, M., 2017, 340–361  mathnet  crossref  mathscinet
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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