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On uniform exponential stability of linear skew-product semiflows in Banach spaces. (English) Zbl 1032.34046

The authors give necessary and sufficient conditions for the uniform exponential stability of linear skew-product semiflows which may be generated by linear evolution equations in Banach spaces. This is done by employing Banach function spaces. Generalizations of some well-known results of Datko, van Neerven, Rolewicz and Zabczyk are obtained.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47D03 Groups and semigroups of linear operators
93D20 Asymptotic stability in control theory
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Full Text: Euclid