Geodesic
Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum
Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 42-53

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1992-002-2
Mots-clés : 47A56, 15A22 
Barkwell, Lawrence; Lancaster, Peter; Markus, Alexander S. Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum. Canadian journal of mathematics, Tome 44 (1991) no. 1, pp. 42-53. doi: 10.4153/CJM-1992-002-2
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