Abstract:
A spectral problem for a multiple differentiation operator with integral perturbation of boundary value conditions which are regular but not strongly regular is considered in the paper. The feature of the problem is the absence of the basis property of the system of root vectors. A characteristic determinant of the spectral problem is constructed. It is shown that absence of the basis property of the system of root functions of the problem is unstable with respect to the integral perturbation of the boundary value condition.
Keywords:
multiple differentiation operator, integral perturbation of boundary value conditions, basis property, root vectors, system of eigenfunctions and associated functions, eigenvalue, characteristic determinant.
Received: 18.05.2020 Received in revised form: 30.06.2020 Accepted: 04.07.2020
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
Nurlan S. Imanbaev, “On a problem that does not have basis property of root vectors, associated with a perturbed regular operator of multiple differentiation”, J. Sib. Fed. Univ. Math. Phys., 13:5 (2020), 568–573
\Bibitem{Ima20}
\by Nurlan~S.~Imanbaev
\paper On a problem that does not have basis property of root vectors, associated with a perturbed regular operator of multiple differentiation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 5
\pages 568--573
\mathnet{http://mi.mathnet.ru/jsfu863}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-5-568-573}
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https://www.mathnet.ru/eng/jsfu863
https://www.mathnet.ru/eng/jsfu/v13/i5/p568
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