Abstract
We consider evolution families (U(t, s)) of bounded, linear operators on a Banach space X and associate to it an evolution semigroup (T(t)) t≥0 defined by
on the weighted function space C υ0(ℝ, X). In the case of Lipschitz continuity of (U(t, s)) we characterize the generator of this semigroup (T(t)) t≥0 and thus obtain a family of operators A(t) ∈ ℒ(X) such that (U(t,s)) solves the non-autonomous Cauchy problem
This paper is part of a research project supported by the Deutsche Forschungsgemeinschsft DFG.
The support of DAAD is gratefully acknowledged.
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Dedicated to Professor A.C. Zaanen in occasion of his 80th birthday.
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Nagel, R., Rhandi, A. (1995). A Characterization of Lipschitz Continuous Evolution Families on Banach Spaces. In: Huijsmans, C.B., Kaashoek, M.A., Luxemburg, W.A.J., de Pagter, B. (eds) Operator Theory in Function Spaces and Banach Lattices. Operator Theory Advances and Applications, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9076-2_14
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DOI: https://doi.org/10.1007/978-3-0348-9076-2_14
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