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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