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On the proof of characterizations of the exponential dichotomy
Authors:Nguyen Van Minh
Affiliation:Department of Mathematics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182, Japan
Abstract:We describe explicitly the generator of the evolutionary semigroup associated with the evolutionary operator generated by the linear differential equation $x'(t)=A(t)x(t)$. From this we give a short proof of some known characterizations of the exponential dichotomy of the above mentioned equation.

Keywords:Evolutionary family   evolutionary semigroup   exponential dichotomy
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