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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, Volume 10, Issue 2, Pages 24–34
DOI: https://doi.org/10.18500/1816-9791-2010-10-2-24-34
(Mi isu18)
 

This article is cited in 5 scientific papers (total in 5 papers)

Mathematics

On multiple completeness of the root functions for a class of the pencils of differential operators

V. S. Rykhlov

Saratov State University, Chair of Differential Equations and Applied Mathematics
Full-text PDF (241 kB) Citations (5)
References:
Abstract: A polinomial pencil of ordinary differential operators of $n$-th order generated by a homogeneous differential expression with constant coefficients and by two-point boundary conditions of a special structure with $l$ conditions in zero only ($1\le l\le n-1$) is considered in the space $L_2[0,1]$. The case is studied, when the roots of the characteristic equation lie on a ray coming fromthe origin. A sufficient condition of $m$-fold completeness of the system of root functions for $m\le n-l$ in the space $L_2[0,1]$ is found. An accuracy of obtained result is shown.
Key words: pencil of ordinary differential operators, two-point boundary conditions, homogeneous differential expression with constant coefficients, multiple completeness of system of root functions, multiple completeness of system of eigen- and associated functions.
Bibliographic databases:
Document Type: Article
UDC: 517.927.25
Language: Russian
Citation: V. S. Rykhlov, “On multiple completeness of the root functions for a class of the pencils of differential operators”, Izv. Saratov Univ. Math. Mech. Inform., 10:2 (2010), 24–34
Citation in format AMSBIB
\Bibitem{Ryk10}
\by V.~S.~Rykhlov
\paper On multiple completeness of the root functions for a~class of the pencils of differential operators
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2010
\vol 10
\issue 2
\pages 24--34
\mathnet{http://mi.mathnet.ru/isu18}
\crossref{https://doi.org/10.18500/1816-9791-2010-10-2-24-34}
\elib{https://elibrary.ru/item.asp?id=14455320}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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