“Integrated semigroups” and integrated solutions to abstract Cauchy problems☆

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Abstract

Concepts which have been developed in the theory of weakly∗ continuous semigroups on dual Banach spaces are extended to “integrated semigroups.” The relation to integrated solutions of homogeneous and inhomogeneous abstract Cauchy problems is established. The results are illustrated for the wave equation in L2(Rm).

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Supported by a Heisenberg scholarship of “Deutsche Forschungsgemeinschaft”.

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