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Representation theorem for mild \(C\)-existence families. (English) Zbl 1123.47305
The paper contains a representation theorem for exponentially bounded mild \(C\)-existence families, generalizing the analogous result of Tanaka and Miyadera for exponentially bounded \(C\)-semigroups. By means of the new theorem, a simple proof of a construction theorem for \(C\)-semigroups is obtained.
MSC:
47D60 \(C\)-semigroups, regularized semigroups
47D62 Integrated semigroups
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