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 $$ \mathscr A=\begin{vmatrix} 0 \\ -A_0-D \end{vmatrix}, $$ 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. 
@article{MZM_2008_83_6_a10,
     author = {C. Trunk},
     title = {Spectral {Theory} for {Operator} {Matrices} {Related} to {Models} in {Mechanics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {923--932},
     publisher = {mathdoc},
     volume = {83},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_6_a10/}
}
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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/