Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces

Details Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces

1993-07-08

arxiv.org/abs/math/9307201v2

J. Func. Anal. 127, (1995), 173-197

Mathematics

Functional Analysis

Scientific paper

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 the investigating of the evolutionary semigroup is developed and applied to describe the hyperbolicity (exponential dichotomy) of the nonautonomuos equation. File Length: 68K

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