摘要
基于双连续半群概念,引入一致双连续半群序列概念,借助Laplace变换和Trotter-Kato定理,考察双连续n次积分C余弦函数与C-预解式之间的关系,得到逼近定理的稳定性条件,进而得出双连续n次积分C余弦函数逼近定理.从而对Banach空间强连续半群逼近定理和双连续半群逼近定理进行了推广,为相应抽象的Cauchy问题提供了解决方案.
Based on the concept of bi-continuous semigroups,a uniformly bi-continuous sequence of semigroups was presented.With Trotter-Kato theorem and Laplace transformation,we obtain the approximation theorem for bi-continuous n-times integrated C-cosine functions by analyzing the relations between bi-continuous n-times integrated C-cosine functions and its resolvent to get stability condition for the approximation theorem and then generalize the approximation theorem for the strong continuous semigroups on Banach space and bi-continuous semigroups,providing a kind of solution for its relative abstract Cauchy problems.
出处
《应用泛函分析学报》
CSCD
2010年第3期249-253,共5页
Acta Analysis Functionalis Applicata
关键词
双连续半群
一致双连续半群
n次积分C余弦函数
预解式
逼近定理
bi-continuous semigroups
uniformly bi-continuous sequence of semigroups
n-times integrated C-cosine functions
resolvent
approximation theorem
