Abstract:
We consider a direct spectral problem for an operator having a non-nuclear resolvent and perturbed by the bounded operator with multiple spectrum. A similar problem was considered earlier for an operator with a single spectrum. The method of regularized traces is used as a method of solution. This method can not be applied directly to the problem. We propose to introduce the relative resolvent of the operator. A spectral problem of the form (M+P)u=Lu is obtained. In this case, the operator L is such that the relative resolvent of the operator is a nuclear operator. As a result of applying the resolvent method to the relative spectrum of the perturbed operator, we obtain relative eigenvalues of the perturbed operator with non-nuclear resolvent.
Citation:
E. V. Kirillov, G. A. Zakirova, “A direct spectral problem for L-spectrum of the perturbed operator with a multiple spectrum”, J. Comp. Eng. Math., 4:3 (2017), 19–26
\Bibitem{KirZak17}
\by E.~V.~Kirillov, G.~A.~Zakirova
\paper A direct spectral problem for $L$-spectrum of the perturbed operator with a multiple spectrum
\jour J. Comp. Eng. Math.
\yr 2017
\vol 4
\issue 3
\pages 19--26
\mathnet{http://mi.mathnet.ru/jcem96}
\crossref{https://doi.org/10.14529/jcem170303}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3708701}
\elib{https://elibrary.ru/item.asp?id=30289924}
Linking options:
https://www.mathnet.ru/eng/jcem96
https://www.mathnet.ru/eng/jcem/v4/i3/p19
This publication is cited in the following 1 articles:
E. V. Kirillov, G. A. Zakirova, “Spectral problem for a mathematical model of hydrodynamics”, J. Comp. Eng. Math., 5:1 (2018), 51–56
Citation in format AMSBIB
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