论文信息 - Characterization of Exponential Stability of a Semigroup of Operators in Terms of Its Action by Convolution on Vector-Valued Function Spaces overR+

Characterization of Exponential Stability of a Semigroup of Operators in Terms of Its Action by Convolution on Vector-Valued Function Spaces overR+

Abstract 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 and only if[formula]where AP ( R + , X ) is the space of X -valued almost periodic functions on R + .

J. Neerven | J. M. A. M. van Neerven

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