Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces
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Publication:6502046
arXivmath/9307201MaRDI QIDQ6502046
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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
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