n次积分C-半群的收敛性  

Convergence of n-Times Integral C-Semigroups

作　　者：张祥芝[1] 宋晓秋[1] 刘钧文[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《中国矿业大学学报》2006年第3期423-426,共4页Journal of China University of Mining & Technology

基　　金：中国矿业大学校科研基金项目(A200402)

摘　　要：讨论了指数有界的n次积分C-半群的收敛性和算子列的逼近问题.证明了在同一空间上,不同n次积分C-半群的生成元可以交换.给出了误差估计的积分表示.由此得出:Banach空间Xk上n次积分C-半群序列Sk(t)强收敛于Banach空间X上n次积分C-半群S(t)的充分条件是其生成元序列Ak强收敛于A,并将这一结论推广到一般的Banach空间序列上.Convergence for exponentially bounded n-times integrated C-semigroups and approximation problem for a sequence of operators were discussed. The interchangeability of generators on the same space for different n -times integrated C -semigroups was proved. The integral representation of error estimate was obtained, which results in the main theorem as follows： an exponentially bounded n -times integrated C-semigroup S（t） on a Banach space X was approximated by a sequence of exponentially bounded n times integrated C-semigroups Sk （t） on spaces Xk if and only if Ak converges to A. The result is generalized to a sequence of Banach spaces.

关 键 词：抽象柯西问题 n次积分C-半群 生成元 收敛 

分 类 号：O177[理学—数学]