强连续双半群与积分双半群  

ON STRONGLY CONTINUOUS BISEMIGROUPS AND INTEGRATED BISEMIGROUPS

作　　者：许跟起[1] 冯德兴[1] 

机构地区：[1]中国科学院系统科学研究所,北京100080

出　　处：《应用数学学报》2000年第1期63-75,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家攀登计划;山西省教委专项基金

摘　　要：本文研究积分双半群与有界线性算子双半群的关系．证明了Ｂａｎａｃｈ空间X上的指数有界积分双半群可以作为X的某个子空间上具有较强范数拓扑下的有界线性算子强连续双半群的积分，同时也可作为较大空间上具有较弱范数拓扑下的有界线性算子强连续双半群积分的限制．上述结果可以用来解释抽象边值问题弱解的意义．The relationship between integrated bisemigroups and bisemigroups of linear bounded operators is investigated. It is shown that an exponentially bounded integrated bisemigroups can be considered as the integration of a strongly continuous bisemigroup of bounded linear operators in some subspace of a Banach space with stronger norm topology, and also as the restriction of a strongly continuous bisemigroup of bounded linear operators in a bigger space with weaker norm topology. The above result can be used to interpret the meaning of weak solution for some abstract boundary value problems.

关 键 词：强连续双半群 积分双半群 抽象边值问题 

分 类 号：O152.7[理学—数学] O175.8[理学—基础数学]