指数有界双连续n阶α次积分C半群的逼近  

Approximation of bi-continuous n-th orderα-times integration C-semigroups with exponential boundedness

作　　者：贺凯丽 赵华新[1] 刘娟娟 HE Kaili;ZHAO Huaxin;LIU Juanjuan(College 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：《延安大学学报（自然科学版）》2023年第4期78-81,共4页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(71961030);延安大学研究生教改项目(YGYJG2019033)。

摘　　要：利用经典算子半群理论中的研究方法,基于双连续n阶α次积分C半群的生成定理,讨论了指数有界双连续n阶α次积分C半群的逼近定理。{T(t)}_(t≥0),{T_(n)(t)}_(t≥0)分别是由A、A_(n)次生成的指数有界双连续n阶α次积分C半群,在一定条件下,可以得到R_(a)(λ,A_(n))x→R_(a)(λ,A)x与T_(n)(t)x→T(t)x等价。研究结果推广了n阶α次积分C半群相关的逼近定理。By using the method of classical operator semigroup theory,based on the generation theorem of bicontinuous n-th orderα-times integration C-semigroups with exponential boundedness,we acquired approximation theorem of bi-continuous n-th orderα-times integration C-semigroups with exponential boundedness.It is proved if bi-continuous n-th orderα-times integration C-semigroups with exponential boundedness{T(t)}_(t≥0),{T_(n)(t)}_(t≥0)are generated by A,A_(n) respectively,under certain conditions,R_(a)(λ,A_(n))x→R_(a)(λ,A)x and T_(n)(t)x→T(t)x can be obtained.

关 键 词：双连续n阶α次积分C半群 逼近 指数有界 

分 类 号：O177.2[理学—数学]