n阶α次积分C半群扰动的指数有界性  

Exponential Boundedness of Perturbations of n-th Order α-Times Integrated C-semigroups

作　　者：刘乔乔 赵华新[1] LIU Qiaoqiao;ZHAO Huaxin(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：《甘肃科学学报》2022年第2期1-4,共4页Journal of Gansu Sciences

基　　金：国家自然科学基金项目(61763045);延安大学研究生教改项目(YDYJG2019033)。

摘　　要：算子半群及其扰动之间的关系是算子半群理论的一个重要问题。借助半群扰动的相关理论及经典算子理论的研究方法,对A次生成的n阶α次积分C半群{T(t)}t≥0,当B是有界线性算子,C_(B)∈B(X)是单射,在一定条件下,C_(B)^(-1)(A+B)C_(B)也生成n阶α次积分C_(B)半群{T_(B)(t)}t≥0,且{T_(B)(t)}t≥0满足指数有界,最后作T_(B)(t)x和T(t)C_(B)C^(-1)x的差。The relationship between semigroup and its perturbations is an important problem in sub-semigroup operator theory.Using the related theory of semigroup perturbation and the research method of classical operator theory,study object is the n-th orderα-times integrated C-semigroups{T(t)}t≥0 generated by A,if B is a bounded linear operator and C_(B)∈B(X)is a injective operator,C_(B)^(-1)(A+B)C_(B) also generates n-th orderα-times integrated C-semigroups{T_(B)(t)}t≥0 under certain conditions,and{T_(B)(t)}t≥0 satisfies exponential boundedness.Finally,the difference between T_(B)(t)x and T(t)C_(B)C^(-1)x is made.

关 键 词：n阶α次积分C半群 扰动 指数有界 

分 类 号：O177.2[理学—数学]