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

A. S. Markus, V. I. Matsaev

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3 Scopus citations

Abstract

Suppose that H is a normal operator, the pencil L0 (λ) = I- λnHn has a discrete and positive spectrum in the domain Ω(2θ, R) = (λ: larg λ < 2θ, λ > R). and S(λ) is an operator-valued function that is holomorphic in Ω(2θ. R.) and small in comparison to L0(λ) (in a certain sense). A theorem is proved on comparison of the spectra of L(λ) = L0(λ)- S(λ) and L0(λ), i.e., on an estimate of the difference N(r) — N0(r), where N(r) (N0(r)) is the distribution function of the spectrum of L(λ) (L0(λ)) in Ω(θ, p) (p ≥ R). This result implies generalizations of theorems of Keldysh on the asymptotic behavior of the spectrum of a polynomial operator pencil.

Original languageEnglish
Pages (from-to)389-404
Number of pages16
JournalMathematics of the USSR - Sbornik
Volume51
Issue number2
DOIs
StatePublished - 28 Feb 1985
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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