An Integrability Condition on the Resolvent for Hyperbolicity of the Semigroup

✍ Scribed by M.A. Kaashoek; S.M.V. Lunel

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 866 KB
• Volume: 112
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1994.1109

✦ Synopsis

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, we discuss three examples. 1994 Academic Press. Inc.