算子半群逼近及收敛速度的几个估计式  

Some Estimators About Approximations and Convergent Rates for Operator Semigroups

作　　者：荣嵘[1] 宋晓秋[1] 林晓庆[1] 朱华[2] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008 [2]中国矿业大学材料科学与工程学院,江苏徐州221008

出　　处：《中国矿业大学学报》2006年第2期279-282,共4页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(50475164)

摘　　要：借助于算子值数学期望以及概率论方法,得到了Banach空间上指数有界的C半群的概率表示式,进而利用T ay lor展开式、Holder不等式及适当的随机变量的矩生成函数估计式等工具,以较为简化的形式给出了C半群概率型逼近及收敛速度的估计式.最后,应用所得到的渐近公式,把C0半群中的一些结果,如K endall及Chung公式,推广到C半群.By means of operator-valued mathematical expect and probabilistic methods, the probabilistic representations for exponentially bounded C-semigroups on Banach space are obtained. Then, using Taylor expansion of the semigroup, Holder＇s inequality and estimations of momentgenerating functions of some suitable random variables, some briefly probabilistic approximations and estimations of convergent rates are obtained for C-semigroups. Finally, using these given asymptotic formulas, some results for Co semigroups, such as Kendall formula and Chung formula are generalized to C-semigroups.

关 键 词：C半群 概率型逼近 收敛速度 矩生成函数 

分 类 号：O177.1[理学—数学]