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

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 comparethe properties of the semigroup generated by , and thesequence , , where .We show that if and generate a uniformly bounded,strongly continuous semigroup on a Hilbert space, then is powerbounded. For analytic semigroups we can prove stronger results. If is the infinitesimal generator of an analytic semigroup, thenpower boundedness of is equivalent to the uniform boundedness ofthe semigroup generated by . 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 Export this item as: BibTeXEndNoteHTML CitationReference Manager

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