双连续n次积分C余弦函数的逼近定理  

Approximation Theorem for Bi-continuous n-times Integrated C-Cosine Functions

作　　者：李慧敏[1] 宋晓秋[1] 赵月英[1] 

机构地区：[1]中国矿业大学理学院,徐州221008

出　　处：《应用泛函分析学报》2010年第3期249-253,共5页Acta Analysis Functionalis Applicata

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.

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 

分 类 号：O177[理学—数学]