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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 4, Pages 45–53 (Mi ufa167)  

On a spectral property of irregular pencils

N. F. Valeev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: The present paper introduces the notion of a quasi-regular eigenvalue and a quasi-regular pencil spectrum of finite dimensional operator pencils. It is demonstrated that quasi-regular eigenvalues of irregular pencils are continuous with respect to perturbations of the pencil. Properties of quasi-regular eigenvalues are studied and formulae for calculating a quasi-regular spectrum are obtained.

Keywords: spectral theory of linear operators, irregular pencils, inverse spectral problems, regular spectrum of the operator pencil.

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UDC: 517.4+519.71
Received: 05.05.2012

Citation: N. F. Valeev, “On a spectral property of irregular pencils”, Ufimsk. Mat. Zh., 4:4 (2012), 45–53

Citation in format AMSBIB
\Bibitem{Val12}
\by N.~F.~Valeev
\paper On a~spectral property of irregular pencils
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 4
\pages 45--53
\mathnet{http://mi.mathnet.ru/ufa167}


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