AI 中文总结
该研究针对希尔伯特空间上生成元满足广义Kreiss预解条件的C0半群，建立了统一增长速率界，改进了已有估计并刻画了超线性增长行为的转变。
AI 中文摘要
本文在注记中建立了希尔伯特空间上生成元满足广义Kreiss预解条件的C0半群算子范数的统一增长速率，该界包含并改进了文献中若干已知估计，尤其能刻画不同超线性增长行为间的转变。
英文摘要
In this note we establish a unified growth rate for the operator norm of $C_0$-semigroups on Hilbert spaces whose generators satisfy the generalized Kreiss resolvent condition. Our bound contains and improves several known estimates in the literature. In particular, it captures the transition between different super-linear growth behaviors.
