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Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum

Published online by Cambridge University Press:  20 November 2018

Lawrence Barkwell ,
Peter Lancaster  and
Alexander S. Markus
Lawrence Barkwell
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4
Peter Lancaster
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4
Alexander S. Markus
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer Sheva, Israel
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Abstract

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Eigenvalue problems for selfadjoint quadratic operator polynomials L(λ) = Iλ2 + Bλ+ C on a Hilbert space H are considered where B, C∈ℒ(H), C >0, and |B| ≥ kI + k-l C for some k >0. It is shown that the spectrum of L(λ) is real. The distribution of eigenvalues on the real line and other spectral properties are also discussed. The arguments rely on the well-known theory of (weakly) hyperbolic operator polynomials.

Keywords

47A5615A22
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 42 - 53
Copyright
Copyright © Canadian Mathematical Society 1991

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