On analytic integrated semigroups

Marko Kostić

The known definition of an analytic $n$-times integrated semigroup is reconsidered and one superfluous condition is removed. It is proved that every densely defined generator of an exponentially bounded, analytic $n$-times integrated semigroup of angle $\alpha$ with the appropriate growth rate at zero is also the generator of an analytic $C_0$-semigroup of the same angle.