Geodesic
Spectral Theory for Operator Matrices Related to Models in Mechanics
Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 923-932

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We derive various properties of the operator matrix $$ \mathscr A=\begin{vmatrix} 0&I \\ -A_0&-D \end{vmatrix}, $$ where $A_0$ is a uniformly positive operator and $A_0^{-1/2}DA_0^{-1/2}$ is a bounded nonnegative operator in a Hilbert space $H$. Such operator matrices are associated with second-order problems of the form $\ddot z(t)+A_0z(t)+D\dot z(t)=0$, which are used as models for transverse motions of thin beams in the presence of damping.
Keywords: operator matrices, second-order partial differential equations, spectrum, Riesz basis, definitizable operator, Krein space, analytic semigroup. 
C. Trunk. Spectral Theory for Operator Matrices Related to Models in Mechanics. Matematičeskie zametki, Tome 83 (2008) no. 6, pp. 923-932. http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a10/
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