| n次积分C-半群的收敛性 |
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| 引用本文： | 张祥芝,宋晓秋,刘钧文.n次积分C-半群的收敛性[J].中国矿业大学学报,2006,35(3):423-426. |
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| 作者姓名： | 张祥芝 宋晓秋 刘钧文 |
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| 作者单位： | 中国矿业大学,理学院,江苏,徐州,221008 |
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| 基金项目： | 中国矿业大学校科研和校改项目 |
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| 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．证明了在同一空问上，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．
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| 关 键 词： | 抽象柯西问题 n次积分C-半群 生成元 收敛 |
| 文章编号： | 1000-1964(2006)01-0423-04 |
| 收稿时间： | 12 9 2004 12:00AM |
| 修稿时间： | 2004年12月9日 |
Convergence of n-Times Integral C-Semigroups |
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| ZHANG Xiang-zhi,SONG Xiao-qiu,LIU Jun-wen.Convergence of n-Times Integral C-Semigroups[J].Journal of China University of Mining & Technology,2006,35(3):423-426. |
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| Authors: | ZHANG Xiang-zhi SONG Xiao-qiu LIU Jun-wen |
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| Abstract: | 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 S_k(t) on spaces X_k if and only if A_k converges to A.The result is generalized to a sequence of Banach spaces. |
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| Keywords: | abstract Cauchy problem n-times integrated C-semigroups generator convergence |
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