On the Strong Kreiss Resolvent Condition
✍ Scribed by Alexander Gomilko, Jaroslav Zemánek
- Book ID
- 120950647
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2011
- Tongue
- English
- Weight
- 215 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1661-8254
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let E be a compact subset of the unit circle. We determine the extremal rate of growth of ðjjT n jjÞ n51 for Banach-space operators T satisfying the resolvent condition jjðT À lIÞ À1 jj4 const: distðl; EÞ ðjlj > 1Þ: This includes, as extreme cases, the Kreiss condition E ¼ T and the Ritt condition
In this paper, we present necessary and sufficient conditions on the. resolvent of the generator of a strongly continuous semigroup in order that the corresponding semigroup is hyperbolic. The proof is based on a new characterization of the growth bound in terms of the resolvent. As an application,