On the proof of characterizations
of the exponential dichotomy
Author: Nguyen Van Minh
Journal: Proc. Amer. Math. Soc. 127 (1999), 779-782
MSC (1991): Primary 34G10, 47D06; Secondary 47H20
MathSciNet review: 1473675
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Abstract: We describe explicitly the generator of the evolutionary semigroup associated with the evolutionary operator generated by the linear differential equation . From this we give a short proof of some known characterizations of the exponential dichotomy of the above mentioned equation.
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Nguyen Van Minh
Affiliation: Department of Mathematics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182, Japan
Keywords: Evolutionary family, evolutionary semigroup, exponential dichotomy
Received by editor(s): December 20, 1996
Received by editor(s) in revised form: June 20, 1997
Additional Notes: This note was written during the author’s visit to the Institute of Mathematics, University of Tübingen. The support of the Alexander von Humboldt Foundation is gratefully acknowledged. He also thanks R. Nagel and the Division of Functional Analysis at the Institute for their warm hospitality and constant encouragement. Finally, he thanks the referee for the valuable suggestion to improve the presentation of this paper.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society