| 仓定帮,闫守峰,陈藏,魏静.广义算子半群的遍历及概率逼近定理[J].数学年刊A辑,2015,36(4):389~400 |
| 广义算子半群的遍历及概率逼近定理 |
| Ergodic Theory and Probabilistic Approximations forGeneralized Operator Semigroups |
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| DOI： |
| 中文关键词: 广义算子半群, 遍历, 概率逼近 |
| 英文关键词:Generalized operator semigroups, Ergodic, Probabilistic approximation |
| 基金项目:本文受到中央高校基本科研业务基金(No.3142012022, No.3142013039, No.3142014039,
& No.314201 4017)和华北科技学院重点学科建设基金(No,HKXJZD201402)的资助. |
| Author Name | Affiliation | E-mail | | CANG Dingbang | Department of Basic, North China Institute of Science and Technology, Beijing
101601, China. | cdbjd@163.com; | | YAN Shoufeng | Department of Basic, North China Institute of Science and Technology, Beijing
101601, China. | yanshoufeng@ncist.edu.cn; | | CHEN Cang | Department of Dean’s, North China Institute of Science and Technology, Beijing
101601, China. | cc@ncist.edu.cn | | WEI Jing | Department of Basic, North China Institute of Science and Technology, Beijing
101601, China. | weijing@ncist.edu.cn |
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| 中文摘要: |
| 首先给出了广义算子半群的 Abel-\!\!遍历和Ces\`{a}ro-\!\!遍历的定义, 对两种遍历的性质进行了刻画, 研究了两种遍历的等价条件. 其次, 利用Pettis积分、
算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式. |
| 英文摘要: |
| The definition of Abel-ergodic and Ces`aro-ergodic about generalized operator
semigroups are given and some characteristics of two ergodicities are discussed. Then the
equivalence conditions of two ergodicities are obtained. At last, by means of the Pettis
integral, the operator-valued mathematical expect and the generalized continuous modified
modulus, the probabilistic approximation and convergent rates are given for generalized
operator semigroups. |
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