Abel平均的幂收敛性
Power convergence of Abel averages
摘要：
在复巴拿赫空间中，给出了离散和强连续半群$T^k$和$T_t$的Abel平均在算子范数下幂收敛的充要条件.这些结果也涵盖了$T$是无界的情况下，相应的阿贝尔平均定义的手段，$T$的预解式。他们补充了经典的结果迈克尔林建立相应的有界$T$收敛的充分条件。
英文摘要：
Necessary and sufficient conditions are presented for the Abel averages of discrete and strongly continuous semigroups, $T^k$ and $T_t$, to be power convergent in the operator norm in a complex Banach space. These results cover also the case where $T$ is unbounded and the corresponding Abel average is defined by means of the resolvent of $T$. They complement the classical results by Michael Lin establishing sufficient conditions for the corresponding convergence for a bounded $T$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
