Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analyticity and Riesz basis property of semigroups associated to damped
  vibrations   Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract
Hilbert space are considered. Such equations are often used as a model for
transverse motions of thin beams in the presence of damping. We derive various
properties of the operator matrix $A$ associated with the second order problem
above. We develop sufficient conditions for analyticity of the associated
semigroup and for the existence of a Riesz basis consisting of eigenvectors and
associated vectors of $A$ in the phase space.

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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th