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Exponential Stability of Semigroups Related to Operator Models in Mechanics

โœ Scribed by R. O. Griniv; A. A. Shkalikov

Book ID
111538813
Publisher
SP MAIK Nauka/Interperiodica
Year
2003
Tongue
English
Weight
141 KB
Volume
73
Category
Article
ISSN
0001-4346

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Characterization of Exponential Stabilit
Characterization of Exponential Stability of a Semigroup of Operators in Terms of Its Action by Convolution on Vector-Valued Function Spaces overR+
โœ J.M.A.M. van Neerven ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 741 KB

It is proved that a C 0 -semigroup T=[T(t)] t 0 of linear operators on a Banach space X is uniformly exponentially stable if and only if it acts boundedly on one of the spaces L p (R + , X) or C 0 (R + , X) by convolution. As an application, it is shown that T is uniformly exponentially stable if an