Abstract
Let $A$ be the generator of an $n$-times integrated semigroup $T(\cdot)$ and let $r \in \mathbb{N}$. We first prove the equivalence of Riemann, Peano, and Taylor operators, which are three different expressions of the $r$-th power of $A_1$, the part of $A$ in the closure of the domain $D(A)$ of $A$. Then we discuss optimal and non-optimal rates of approximation of $T(\cdot)x$ for $x \in D(A^{r−1}_{1})$, via the $(n+r)$-th Taylor expansion of $T(\cdot)$ in terms of $A^k_1$, $k = 0, \ldots, r−1$.
Citation
Jung-Chan Chang. Sen-Yen Shaw. "POWERS OF GENERATORS AND TAYLOR EXPANSIONS OF INTEGRATED SEMIGROUPS OF OPERATORS." Taiwanese J. Math. 10 (1) 101 - 115, 2006. https://doi.org/10.11650/twjm/1500403802
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