Stability of C-regularized Semigroups  

作　　者：MiaoLI QuanZHENG 

机构地区：[1]DepartmentofMathematics,SichuanUniversity,Chengdu610064,P.R.China [2]DepartmentofMathematicsCentralChina(Huazhong)NormalUniversity,Wuhan430079,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2004年第5期821-828,共8页数学学报（英文版）

基　　金：supported by the NSF of China;supported by TRAPOYT and the NSF of China(No.10371046)

摘　　要：Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.Let T=(T(t))_(t≥0)be a bounded C-regularized semigroup generated by A on a Banach space X and R(C)be dense in X.We show that if there is a dense subspace Y of X such that for every x ∈ Y,σ_u(A,Cx),the set of all points λ ∈ iR to which(λ-A)^(-1)Cx can not be extended holomorphically,is at most countable and σ_r(A)∩ iR=(?),then T is stable.A stability result for the case of R(C)being non-dense is also given.Our results generalize the work on the stability of strongly continuous semigroups.

关 键 词：C-regularized semigroups Generators STABLE Hille-Yosida space 

分 类 号：O152[理学—数学] O177.2[理学—基础数学]