# Continuous-time Kreiss resolvent condition on infinite-dimensional spaces

Eisner, T. and Zwart, H.J. (2006) Continuous-time Kreiss resolvent condition on infinite-dimensional spaces. Mathematics of Computation, 75 (256). pp. 1971-1985. ISSN 0025-5718

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 Abstract: Given the infinitesimal generator of a -semigroup on the Banach space which satisfies the Kreiss resolvent condition, i.e., there exists an such that for all complex with positive real part, we show that for general Banach spaces this condition does not give any information on the growth of the associated -semigroup. For Hilbert spaces the situation is less dramatic. In particular, we show that the semigroup can grow at most like . Furthermore, we show that for every there exists an infinitesimal generator satisfying the Kreiss resolvent condition, but whose semigroup grows at least like . As a consequence, we find that for with the standard Euclidian norm the estimate cannot be replaced by a lower power of or . Item Type: Article Faculty: Electrical Engineering, Mathematics and Computer Science (EEMCS) Research Group: Link to this item: http://purl.utwente.nl/publications/63837 Official URL: http://www.ams.org/mcom/2006-75-256/S0025-5718-06-01862-X/home.html Export this item as: BibTeXEndNoteHTML CitationReference Manager

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