广义算子半群渐近行为及其强弱稳定性

摘要

首先给出了由Banach空间有界线性算子引导的广义算子半群的定义及其性质；其次研究广义算子半群的渐近表达式；最后研究了广义算子半群的强弱稳定性,给出了广义算子半群强弱稳定性等价的条件.%First, the concept of generalized operator semigroups and some properties are given. Then by studying the stability of generalized operator semigroups, the asymptotic behavior representations for generalized operator semigroups are obtained. In addition, the equivalent conditions for strong stability and weak stability of generalized operator semigroups are also given.