A Formula for n-times Integrated Semigroups $\boldsymbol{(\boldsymbol n\boldsymbol\in \mathbb N)}$
DOI:
https://doi.org/10.5644/SJM.04.1.11Keywords:
Linear operator on a Banach space, strongly continuous semigroup, exponentially bounded $n$-times integrated semigroupAbstract
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
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References
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