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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

Tadzhik State University

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
Received: 01.04.1970

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}


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