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Laplace transforms and \(\alpha\)-times integrated semigroups. (English) Zbl 0766.47013

Summary: We introduce \(\alpha\)-times integrated semigroups for positive real numbers \(\alpha\). A Hille-Yosida type characterization of their generators is given as a consequence of a vector-valued version of Widder’s theorem. Finally the connection between \(\alpha\)-times integrated semigroups and the abstract Cauchy problem is investigated.

MSC:

47D06 One-parameter semigroups and linear evolution equations
34G10 Linear differential equations in abstract spaces
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