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双连续正则预解算子族的生成及逼近定理

The Generation and Approximation Theorems for Bi-Continuous Regularized Resolvent Operator Families
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摘要 传统的半群理论研究很多时候要求半群是Banach空间上的强连续半群,在实际研究中发现有些问题所对应的半群并不是强连续的,可以在Banach空间上赋予一个比范数拓扑粗的局部凸拓扑τ,使得半群在拓扑τ下强连续.基于此在给出了Banach空间上双连续正则预解算子族概念及其性质的基础上,重点讨论双连续正则预解算子族的生成及逼近定理. For many applications of operator semigroups,strong continuity with respect to the norm of a Banach space is a too strong requirement.In fact,there exists a class operator semigroups which the usual strong continuity fails to hold and then the concept of bi-continuous semigroups is introduced.Based on the theories of bi-continuous semigroups and regularized resolvent operator families,the concept of bi-continuous regularized resolvent operator families is presented,then the generation and approximation theorems for bi-continuous regularized resolvent operator families are studied especially.
作者 陈藏 葛世刚 刘海生 仓定帮
机构地区 华北科技学院教务处 华北科技学院基础部
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第6期844-849,共6页 Journal of Sichuan Normal University（Natural Science）
基金 中央高校基本科研资助基金(3142014039 3142013039和3142014127)资助项目
关键词 双连续正则预解算子族 生成定理 逼近定理 bi-continuous regularized resolvent operator generation theorems approximation theorems
分类号 O177.2 [理学—基础数学]
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参考文献15

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二级参考文献21

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共引文献6

四川师范大学学报（自然科学版）
2014年 第6期

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