关于局部α次积分C半群的一些性质

Some properties about local α-times integrated C-semigroups

算子半群的基本理论是泛函分析的一个内容丰富的重要分支。1987年Adrendt首先提出了一次积分半群,并且对一次积分半群的性质进行了讨论。1988年,Neubrander首次引入了n次积分半群的概念,随着研究的进一步深入,又出现了积分C-半群,n次积分C-半群,α次积分C-半群,局部n次积分C-半群及局部α次积分C-半群等,其中郑权对α次积分C-半群的扰动做了深入的研究,这为后来学者对局部α次积分C-半群的研究奠定了基础。在上述理论的基础上,利用局部α次积分C-半群的定义,并且结合α次累积分及卷积性质,得出局部α次积分C-半群的几个性质定理。

The basic theory of the operator semigroups is an important branch of functional analysis.In 1987,the integrated semigroups and its properties were first proposed and explored by Adrendt.In 1988,the concept of n-time integrated semigroups was first introduced by Neubrander.With further research,integrated C-semigroups,n-time integrated C-semigroups,α-time integrated C-semigroups,local n-time integrated C-semigroups,local α-time integrated C-semigroups,etc have appeared successively.Zheng Quan researched the perturbations of α-time integrated semigroups,which laid the foundation for the later scholars studying local α-time integrated C-semigroups.According to the definition of local α-time integrated C-semigroups,and combining with the properties of α-time repeated integral and convolution formula obtained,some theorem of local α-time integrated C-semigroups are given.