On twofold completeness of inherent and adjoined elements of a quadratic operator bundle

1973 ◽  
Vol 7 (1) ◽  
pp. 84-86
Author(s):  
S. Ya. Yakubov
Keyword(s):  
Quadratic Operator ◽  
Operator Bundle

scholarly journals Elliptic Quadratic Operator Equations

2018 ◽  
Vol 159 (1) ◽  
pp. 29-74 ◽  
Author(s):  
Rasul Ganikhodzhaev ◽  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Operator Equations ◽  
Quadratic Operator

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

1981 ◽  
Vol 30 (3) ◽  
pp. 676-684 ◽  
Author(s):  
A. A. Shkalikov
Keyword(s):  
Quadratic Operator ◽  
Operator Pencils

Quadratic operator inequalities and linear-fractional relations

2007 ◽  
Vol 41 (4) ◽  
pp. 314-317 ◽  
Author(s):  
V. A. Khatskevich ◽  
M. I. Ostrovskii ◽  
V. S. Shulman
Keyword(s):  
Quadratic Operator ◽  
Operator Inequalities

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

1991 ◽  
Vol 44 (1) ◽  
pp. 42-53 ◽  
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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