𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces

✍ Scribed by Y. Latushkin; S. Montgomerysmith

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
917 KB
Volume
127
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

We present a spectral mapping theorem for continuous semigroups of operators on any Banach space (E). The condition for the hyperbolicity of a semigroup on (E) is given in terms of the generator of an evolutionary semigroup acting in the space of (E)-valued functions. The evolutionary semigroup generated by the propagator of a nonautonomous differential equation in (E) is also studied. A "discrete" technique for investigating the evolutionary semigroup is developed and applied in describing the hyperbolicity (exponential dichotomy) of the nonautonomous equation. r. 1995 Academic Press, Inc

πŸ“œ SIMILAR VOLUMES

Nonsymmetric Ornstein–Uhlenbeck Semigrou
Nonsymmetric Ornstein–Uhlenbeck Semigroups in Banach Spaces
✍ J.M.A.M van Neerven πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 549 KB

Let E be a separable real Banach space and let Q # L(E\*, E) be positive and symmetric. Let S=[S(t)] t 0 be a C 0 -semigroup on E We study the relations between the reproducing kernel Hilbert spaces associated with the operators Q t := t 0 S(s) QS\*(s) ds. Under the assumption that these operators a