Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line |
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Authors: | Nguyen Van Minh Frank Räbiger Roland Schnaubelt |
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Affiliation: | (1) Department of Mathematics, University of Hanoi, 90 Nguyen Trai, Hanoi, Vietnam;(2) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany |
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Abstract: | LetU=(U(t, s))tsO be an evolution family on the half-line of bounded linear operators on a Banach spaceX. We introduce operatorsGO,GX andIX on certain spaces ofX-valued continuous functions connected with the integral equation, and we characterize exponential stability, exponential expansiveness and exponential dichotomy ofU by properties ofGO,GX andIX, respectively. This extends related results known for finite dimensional spaces and for evolution families on the whole line, respectively.This work was done while the first author was visiting the Department of Mathematics of the University of Tübingen. The support of the Alexander von Humboldt Foundation is gratefully acknowledged. The author wishes to thank R. Nagel and the Functional Analysis group in Tübingen for their kind hospitality and constant encouragement.Support by Deutsche Forschungsgemeinschaft DFG is gratefully acknowledged. |
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Keywords: | Primary 34G10 47D06 Secondary 47H20 |
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