指数有界C余弦算子函数的概率型表示

J4 ›› 2010, Vol. 45 ›› Issue (4): 77-81.

指数有界C余弦算子函数的概率型表示

赵月英,宋晓秋*

中国矿业大学理学院, 江苏徐州 221116

收稿日期:2009-07-06 出版日期:2010-04-10 发布日期:2010-05-19
通讯作者: 宋晓秋(1963-),男,教授,研究方向为算子半群.
作者简介:赵月英(1984-),女,硕士研究生,研究方向为算子半群.Email:zlyue2006@126.com
基金资助:
国家自然科学基金资助项目(10671205)

The probabilistic approximations for exponentially bounded C-Cosine functions

ZHAO Yue-ying, SONG Xiao-qiu*

College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Received:2009-07-06 Online:2010-04-10 Published:2010-05-19

摘要/Abstract

摘要：

利用指数有界C余弦算子函数｛C(t);t∈R｝的性质,推出了指数有界C余弦算子函数的Taylor展开式,然后借助Pettis积分、Holder不等式及随机变量的矩生成函数等工具,得到了指数有界C余弦算子函数的概率逼近公式及Vonorovskaya型渐近公式。

关键词: 指数有界C余弦算子函数; Taylor展开式; 概率型逼近; Vonorovskaya型渐近公式

Abstract:

Based on properties of exponentially bounded C-Cosine functions, the Taylor expansion formula for exponentially bounded C-Cosine functions is obtained. By means of Pettis integral, Holder inequality and moment-generating functions of some suitable random variables, the probabilistic approximations and Vonorovskaya type asymptotic formula for C-Cosine functions are given.

Key words: exponentially bounded C-Cosine functions; Taylor expansion formula; probabilistic approximations; Vonorovskaya type asymptotic formula

赵月英,宋晓秋*. 指数有界C余弦算子函数的概率型表示[J]. J4, 2010, 45(4): 77-81.

ZHAO Yue-ying, SONG Xiao-qiu*. The probabilistic approximations for exponentially bounded C-Cosine functions[J]. J4, 2010, 45(4): 77-81.

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