关于解析C-半群的扰动  

A New Perturbation Theorem for Analytic-Semigroups

作　　者：杨延涛[1] 赵华新[1] 

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：《沈阳师范大学学报（自然科学版）》2011年第1期22-24,共3页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10801023);陕西省教育厅专项科研计划项目(08JK497)

摘　　要：当C具有非稠值域时,在解析半群与C半群的扰动理论基础上,利用可闭化算子的概念及性质研究了解析C-半群的扰动问题。并在不同条件下证明解析C半群的Phillips扰动理论仍成立,从而得到其新的扰动定理。解析C-半群的扰动定理通常情况下要求线性算子A为解析C-半群的无穷小生成元,B为闭线性算子,那么A+BC是解析C-半群的无穷小生成元。在此,由可闭化线性算子与闭线性算子的关系,给出了当B为可闭化线性算子时,A+-BC仍是解析C-半群的无穷小生成元,推广了解析C-半群扰动理论的相关结果,从而为微分方程、分布参数控制系统等相关领域的研究提供了指导资料和参考依据。When C is in the range of non-viscous,based on the perturbations of Csemigroups and analytic semigroups,Perturbation problem of analytic C-semigroups are studied by the concept of closable operator and properties.The Phillips perturbation theoem of analytic C-semigroups is proved under different conditions.So a new perturbation theorem for analytic C-semigroups are obtained.In general,let A be the infinitesimal generator of an analytic C-semigroup,let B be a closed linear operator,then A＋BC is the Infinitesimal generator of an analytic C-semigorp.This paper provides let B be a closable linear oprator,then A＋C is the Infinitesimal generator of an analytic C-semigorp,and the related results of perturbation theorem for analytic C-semigroups are extended,this provided the basic information and reference for the related field of differential equations and distribution parameter control syetems.

关 键 词：解析C-半群 无穷小生成元 可闭化算子 扰动 

分 类 号：O177.31[理学—数学]