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Matematicheskie Zametki, 2008, Volume 83, Issue 6, Pages 923–932
DOI: https://doi.org/10.4213/mzm4841
(Mi mzm4841)
 

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
Full-text PDF (521 kB) Citations (4)
References:
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
English version:
Mathematical Notes, 2008, Volume 83, Issue 6, Pages 843–850
DOI: https://doi.org/10.1134/S0001434608050295
Bibliographic databases:
UDC: 517.958
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm4841
  • https://doi.org/10.4213/mzm4841
  • https://www.mathnet.ru/eng/mzm/v83/i6/p923
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:51
    First page:6
     
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