Spectral properties of a class of quadratic operator pencils

A. I. Miloslavskii

doi:10.1007/bf01082292

Spectral properties of a class of quadratic operator pencils

Functional Analysis and Its Applications ◽

10.1007/bf01082292 ◽

1981 ◽

Vol 15 (2) ◽

pp. 142-144

Author(s):

A. I. Miloslavskii

Keyword(s):

Spectral Properties ◽

Quadratic Operator ◽

Operator Pencils

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Property of the eigenvectors of quadratic operator pencils of being a basis

Mathematical Notes ◽

10.1007/bf01141624 ◽

1981 ◽

Vol 30 (3) ◽

pp. 676-684 ◽

Cited By ~ 2

Author(s):

A. A. Shkalikov

Keyword(s):

Quadratic Operator ◽

Operator Pencils

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On the spectra of some classes of quadratic operator pencils

Contributions to Operator Theory in Spaces with an Indefinite Metric ◽

10.1007/978-3-0348-8812-7_2 ◽

1998 ◽

pp. 23-36 ◽

Cited By ~ 1

Author(s):

V. Adamyan ◽

V. Pivovarchik

Keyword(s):

Quadratic Operator ◽

Operator Pencils

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

Canadian Journal of Mathematics ◽

10.4153/cjm-1992-002-2 ◽

1991 ◽

Vol 44 (1) ◽

pp. 42-53 ◽

Cited By ~ 33

Author(s):

Lawrence Barkwell ◽

Peter Lancaster ◽

Alexander S. Markus

Keyword(s):

Hilbert Space ◽

Real Line ◽

Spectral Properties ◽

Eigenvalue Problems ◽

Real Spectrum ◽

Hyperbolic Operator ◽

Quadratic Operator ◽

Distribution Of Eigenvalues ◽

Quadratic Eigenvalue Problems ◽

Quadratic Eigenvalue

AbstractEigenvalue 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.

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