双连续α次积分C余弦函数的生成定理  

A Generation Theorem for Bi-continuous α-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,江苏徐州221116

出　　处：《中国矿业大学学报》2010年第3期465-470,共6页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(10671205);徐州市科技计划项目(XM08C095);中国矿业大学科技基金项目(OK060156)

摘　　要：基于双连续半群和α次积分C余弦函数的理论,提出了双连续α次积分C余弦函数概念.借助Laplace变换,考察双连续α次积分C余弦函数生成元和预解式之间的关系,以及Hille-Yosida算子和双连续α次积分C余弦函数之间的生成关系,并由此生成关系得出双连续α次积分C余弦函数的生成定理,从而对Banach空间中强连续算子半群的生成定理进行了推广.Based on the theories of bi-continuous semigroups and α-times integrated C cosine functions, the concept of hi-continuous α-times integrated C cosine functions was presented. By the Laplace transformation, the relations between the generator and the resolvent, and the generation relation between Hille-Yosida operators and bi-continuous α-times integrated C co- sine functions were investigated. We obtain the generation theorem for hi-continuous α-times integrated C cosine functions and then generalize the generation theorem for the strong continuous semigroups on Banach space.

关 键 词：双连续α次积分C余弦函数 预解式 生成元 生成定理 

分 类 号：O177[理学—数学]