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 Mat. Zametki, 1972, Volume 12, Issue 4, Pages 403–412 (Mi mz9898)

Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator

Yu. Muratov

Abstract: We obtain asymptotic bounds for the perturbed eigenvalues and eigenvectors of a perturbed linear bounded operator $A(\varepsilon)$, in a Hilbert space under the assumption that $A(\varepsilon)$ is holomorphic at the point $\varepsilon=\varepsilon_0$ and the eigenvalue $\lambda_0=\lambda(\varepsilon_0)$ of the operator $A(\varepsilon_0)$ is isolated and of finite multiplicity. We study certain cases of high degeneracy in the limiting problem, i.e., the case when there are generalized associated vectors.

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English version:
Mathematical Notes, 1972, 12:4, 673–679

Bibliographic databases:

UDC: 517.4

Citation: Yu. Muratov, “Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator”, Mat. Zametki, 12:4 (1972), 403–412; Math. Notes, 12:4 (1972), 673–679

Citation in format AMSBIB
\Bibitem{Mur72} \by Yu.~Muratov \paper Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator \jour Mat. Zametki \yr 1972 \vol 12 \issue 4 \pages 403--412 \mathnet{http://mi.mathnet.ru/mz9898} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=322550} \zmath{https://zbmath.org/?q=an:0251.47026} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 4 \pages 673--679 \crossref{https://doi.org/10.1007/BF01093672}