指数有界双连续n阶α次积分C半群的扰动  

Perturbation of Bi-Continuous n-th Orderα-Times Integration C-Semigroups With Exponentially Boundedness

作　　者：赵华新[1] 贺凯丽 刘娟娟 ZHAO Huaxin;HE Kaili;LIU Juanjuan(School of Mathematics and Computer Science,Yan'an University,Yan'an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《沈阳大学学报（自然科学版）》2024年第1期86-90,共5页Journal of Shenyang University：Natural Science

基　　金：国家自然科学基金资助项目(71961030)。

摘　　要：利用经典算子半群理论中的研究方法,在指数有界双连续α次积分C半群的基础上,讨论了指数有界双连续n阶α次积分C半群的扰动定理。设A为次生成元的指数有界双连续n阶α次积分C半群{T(t)}_(t≥0),B为界线性算子,A、B、C可交换,则在一定条件下,C^(-1)(A+B)C_(B)生成双连续n阶α次积分C半群{T_(B)(t)}_(t≥0),并给出T_(B)(t)的表达式,从而推广了n阶α次积分C半群相关的扰动定理。Based on the classical operator semigroup theory,the perturbation theorem of exponentially bounded bi-continuousα-times integration C-semigroups was discussed.Let A be an exponentially bounded bi-continuous n-th orderα-times integration C-semigroup{T(t)}_(t≥0)of a subgenerator,B be a boundary-property operator,and A,B,C be commutative.Under certain conditions,It was proved that C^(-1)(A+B)C_(B)generates bi-continuous n-th orderα-times integration C-semigroups with exponential boundedness{T_(B)(t)}_(t≥0).The expression for the T_(B)(t)was given,thus generalized the perturbation theorem for the bi-continuous n-th orderα-times integration C-semigroups correlation.

关 键 词：双连续 n阶α次积分C半群 扰动 指数有界 生成元 

分 类 号：O177.2[理学—数学]