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Hyperbolic evolution semigroups on vector valued function spaces

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Abstract

In [13] we characterized exponentially dichotomic evolution operators (U(t,s)) t,s∈ℝ on a Banach spaceE in terms of the spectrum of an associatedC 0-group on anE-valued function space. In this paper we investigate the more general case of hyperbolic evolution families (U(t,s)) t≥s,s∈ℝ and derive a spectral characterization through an associatedC 0-semigroup. We then apply the results to periodic initial value problems and show that the semigroup can be interpreted as a generalized monodromy operator. Furthermore we briefly discuss the spectral properties of aC 0-semigroup associated with an evolution family (U(t, s)) t ≥s≥0.

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  1. Mathematisches Institut, Auf der Morgenstelle 10, D-72076, Tübingen 1, Germany

    René T. Rau

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  1. René T. Rau
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Supported by the Deutsche Forschungsgemeinschaft

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Rau, R.T. Hyperbolic evolution semigroups on vector valued function spaces. Semigroup Forum 48, 107–118 (1994). https://doi.org/10.1007/BF02573658

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  • DOI: https://doi.org/10.1007/BF02573658

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