指数有界n次积分双连续C半群Trotter-Kato逼近

With operator semigroups developing so far, the theory of strong continuous semigroups has been perfected well,but there are many conditions that aren’t strong continuous in the actual study, from the very beginning many situations occured in which the corresponding semigroup is not strongly continuous or the underlying space is not a Banach space. In order to deal with such phenomena, the scholars introduce a whole range of semigroups on Banach spaces having weaker continuity which are strongly continuous semigroups on locally convex spaces.The paper brings in index bounded n-times intergrated bi–continuous C-semigroups on the basis of bi–continuous C-semigroups and index bounded n-time intergrated bi–continuous C-semigroups, abtaining Trotter-Kato approximation for index bounded n-times intergrated bi–continuous C-semigroups through relavent demonstration.