Powers of Generators of Holomorphic Semigroups
Ralph deLaubenfels · Proceedings of the American Mathematical Society · 1987
We show that when the (possibly unbounded) linear operator $- A$ generates a bounded holomorphic semigroup of angle $\theta$, and $n\left ( {\pi /2 - \theta } \right ) < \pi /2$, then $- {A^n}$ generates a bounded holomorphic semigroup of angle $\pi /2 - n\left ( {\pi /2 - \theta } \right )$. When $- A$ generates a bounded holomorphic semigroup of angle $\pi /2$, then, for all $n$, $- {A^n}$ generates a bounded holomorphic semigroup of angle $\pi /2$.