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"Integrated semigroups” and integrated solutions to abstract Cauchy problems. (English) Zbl 0738.47037
Summary: 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 L 2 ( m ).

MSC:
47D06One-parameter semigroups and linear evolution equations