【作者】 秦喜梅；

【导师】 孙国正；

【作者基本信息】 安徽师范大学 ， 基础数学， 2007， 硕士

【摘要】 近年来对有界连续（或一致连续）函数空间上半群的研究,引起了人们对Banach空间上非强连续半群的研究.F.Kuhnemund在Banach空间上另外附加一个比范数拓扑粗的局部凸拓扑,使得半群在这个局部凸拓扑下强连续,由此提出了双连续半群的概念.本文结合双连续半群和n次积分C-半群提出了双连续n次积分C-半群的概念,并给出了其生成元和C-预解式的定义.通过讨论生成元和C-预解式的性质,得到了双连续n次积分C-半群的生成定理.在本文中引入一致双连续n次积分C-半群的概念,并结合生成元和C-预解式间的关系,得到了双连续n次积分C-半群的逼近定理.受A.Pazy的C₀半群指数公式等文献的启发,讨论了双连续n次积分C-半群的表示定理.更多还原

【Abstract】 In the last years,the study of semigroups on spaces of bounded continuous （or uniformly continuous） functions led to consider semigroups for which the usual strong continuity fails to hold on Banach spaces.Kuhnemund considered bi-continuous semigroups,i.e., semigroups are strongly continuous with respect to an additional locally convex topology on a Banach space which is coarser than the norm topology. In this paper,we introduce bi-continuous n-times integrated C-semigroups by combining bi-continuous semigroups and n-times integrated C-semigroups.And we define their generators and C-resolvents. On the basis of their properties,the generation theorem of bi-continuous n-times integrated C-semigroups is obtained.we introduce the concepts of uniformly bi-continuous n-times integrated C-semigroups and combine the relations of generators and C-resolvents,so we gain the approximation theorem of bi-continuous n-times integrated C-semigroups.We debate the representation theorem of bi-continuous n-times integrated C-semigroups enlightened by A.Pazy’s C₀ semigroups exponential formulas and other literatures.更多还原