论文标题
操作员半群的衰减，无限的可采用性和相关的分解估计值
Decay of Operator Semigroups, Infinite-time Admissibility, and Related Resolvent Estimates
论文作者
论文摘要
我们从$ l^p $ - infinite的可接受性和相关的分解估计的角度研究有限的$ C_0 $ -Semigroups的衰减率。在希尔伯特空间设置中，半群轨道的多项式衰减的特征是右半平面中的分解行为。基于$ l^p $ - infinite时间可接受性的类似表征，用于$ 1 \ leq q \ leq q \ leq p <\ infty $。对于Hilbert Space上的多项式稳定$ C_0 $ -Semigroups，我们还为$ l^2 $ -infinite的可接受性提供了足够的条件。
We study decay rates for bounded $C_0$-semigroups from the perspective of $L^p$-infinite-time admissibility and related resolvent estimates. In the Hilbert space setting, polynomial decay of semigroup orbits is characterized by the resolvent behavior in the open right half-plane. A similar characterization based on $L^p$-infinite-time admissibility is provided for multiplication semigroups on $L^q$-spaces with $1 \leq q \leq p < \infty$. For polynomially stable $C_0$-semigroups on Hilbert spaces, we also give a sufficient condition for $L^2$-infinite-time admissibility.
