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.
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- Nguyen Van Minh
- Affiliation: Department of Mathematics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182, Japan
- Email: email@example.com
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 779-782
- MSC (1991): Primary 34G10, 47D06; Secondary 47H20
- DOI: https://doi.org/10.1090/S0002-9939-99-04640-7
- MathSciNet review: 1473675