Hilbert空间上线性斜积半流的一致指数膨胀性的存在条件

Criteria for the existence of uniform exponential expansiveness of linear skew-product semiflows in Hilbert spaces

该文的主要目的是在Hilbert空间中基于线性斜积半流的定义研究其一致指数膨胀的存在条件.应用泛函分析与算子理论相关方法,得到了线性斜积半流满足一致指数膨胀的若干连续时间形式的Lyapunov算子不等式.所得的Lyapunov型结论推广和完善了指数稳定性与指数膨胀性理论中的一些已有结果(如Datko、Pazy、Rolewicz等).

In this paper the existence conditions for uniform exponential expansiveness of linear skew-product semiflows are studied in Hilbert spacesbased on the definition of linear skew-product semiflows.Several continuous-time Lyapunov operator inequalities for uniform exponential expansiveness are obtained via functional analysis and operator theory.The Lyapunov type results extend some well-known conclusions in exponential stability theory and exponential expansiveness theory.