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This article is cited in 4 scientific papers (total in 4 papers)
Spectral Theory for Operator Matrices Related to Models in Mechanics
C. Trunk Technische Universität Berlin
Abstract:
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.
Received: 20.07.2007
Citation:
C. Trunk, “Spectral Theory for Operator Matrices Related to Models in Mechanics”, Mat. Zametki, 83:6 (2008), 923–932; Math. Notes, 83:6 (2008), 843–850
Linking options:
https://www.mathnet.ru/eng/mzm4841https://doi.org/10.4213/mzm4841 https://www.mathnet.ru/eng/mzm/v83/i6/p923
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Abstract page: | 435 | Full-text PDF : | 191 | References: | 51 | First page: | 6 |
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