✦ LIBER ✦
Characterization of Exponential Stability of a Semigroup of Operators in Terms of Its Action by Convolution on Vector-Valued Function Spaces overR+
✍ Scribed by J.M.A.M. van Neerven
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 741 KB
- Volume
- 124
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
✦ Synopsis
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
where AP(R + , X) is the space of X-valued almost periodic functions on R + .