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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 3, Pages 391–406 (Mi msb2027)  

This article is cited in 11 scientific papers (total in 11 papers)

A theorem on comparison of spectra, and spectral asymptotics for a Keldysh pencil

A. S. Markus, V. I. Matsaev

Abstract: Suppose that $H$ is a normal operator, the pencil $L_0(\lambda)=I-\lambda^nH^n$ has a discrete and positive spectrum in the domain $\Omega(2\theta,R)=\{\lambda:\lvert\arg\lambda\rvert<2\theta, |\lambda|>R\}$, and $S(\lambda)$ is an operator-valued function that is holomorphic in $\Omega(2\theta,R)$ and small in comparison to $L_0(\lambda)$ (in a certain sense). A theorem is proved on comparison of the spectra of $L(\lambda)=L_0(\lambda)-S(\lambda)$ and $L_0(\lambda)$, i.e., on an estimate of the difference $N(r)-N_0(r)$, where $N(r)$ ($N_0(r)$) is the distribution function of the spectrum of $L(\lambda)$ ($L_0(\lambda)$) in $\Omega(\theta,\rho)$ ($\rho\geqslant R$). This result implies generalizations of theorems of Keldysh on the asymptotic behavior of the spectrum of a polynomial operator pencil.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:2, 389–404

Bibliographic databases:

UDC: 517.984
MSC: Primary 47A10, 47A55; Secondary 47A53, 47B05, 47B10, 47B15
Received: 23.07.1981

Citation: A. S. Markus, V. I. Matsaev, “A theorem on comparison of spectra, and spectral asymptotics for a Keldysh pencil”, Mat. Sb. (N.S.), 123(165):3 (1984), 391–406; Math. USSR-Sb., 51:2 (1985), 389–404

Citation in format AMSBIB
\by A.~S.~Markus, V.~I.~Matsaev
\paper A~theorem on comparison of spectra, and spectral asymptotics for a~Keldysh pencil
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 3
\pages 391--406
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 2
\pages 389--404

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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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