Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces
arXiv:math/9307201
Abstract
We present a spectral mapping theorem for continuous semigroups of operators on any Banach space . The condition for the hyperbolicity of a semigroup on is given in terms of the generator of an evolutionary semigroup acting in the space of -valued functions. The evolutionary semigroup generated by the propagator of a nonautonomous differential equation in 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