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11. 6. 2024.
A Formula for n-times Integrated Semigroups $\boldsymbol{(\boldsymbol n\boldsymbol\in \mathbb N)}$
Motivated with Hille's first exponential formula for $C_{0}$ semigroups, we prove a formula for $n-$times integrated semigroups. At first we prove a formula for twice integrated semigroup, and, later, we generalize this formula for $n-$times integrated semigroups. 2000 Mathematics Subject Classification. 47D60, 47D62