Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum
- 1 December 1991
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 44 (1) , 42-53
- https://doi.org/10.4153/cjm-1992-002-2
Abstract
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
This publication has 1 reference indexed in Scilit:
- Lectures in Functional Analysis and Operator TheoryPublished by Springer Nature ,1974