Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces
泛函分析
2008-02-03 v2
摘要
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
引用
@article{arxiv.math/9307201,
title = {Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces},
author = {Yuri D. Latushkin and Stephen J. Montgomery-Smith},
journal= {arXiv preprint arXiv:math/9307201},
year = {2008}
}