On the Relation between stability of continuous- and discrete-time evolution equations via the Cayley transform

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Guo, B.Z. and Zwart, H.J. (2006) On the Relation between stability of continuous- and discrete-time evolution equations via the Cayley transform. Integral Equations and Operator Theory, 54 . pp. 349-383. ISSN 0378-620X

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Abstract:n this paper we investigate and compare
the properties of the semigroup generated by $A$, and the
sequence $A_d^n$, $n \in {\mathbb N}$, where $A_d= (I+A)(I-A)^{-1}$.

We show that if $A$ and $A^{-1}$ generate a uniformly bounded,
strongly continuous semigroup on a Hilbert space, then $A_d$ is power
bounded. For analytic semigroups we can prove stronger results. If
$A$ is the infinitesimal generator of an analytic semigroup, then
power boundedness of $A_d$ is equivalent to the uniform boundedness of
the semigroup generated by $A$.
Item Type:Article
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/62874
Official URL:http://dx.doi.org/10.1007/s00020-003-1350-9
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