白噪声分析中广义算子值函数的Bochner-Wick积分  

Bochner-Wick Integrals of Generalized Operator Valued Function in White Noise Analysis

作　　者：韩琦[1] 王才士[1] 成丹[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《应用概率统计》2014年第3期244-256,共13页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(11061032;71261023)资助

摘　　要：白噪声广义算子在白噪声分析理论及其应用中起着十分重要的作用.本文主要讨论了白噪声广义算子值函数的积分及相关问题.主要工作有:引入了广义算子值测度的概念,分别讨论了这种测度在象征和算子p-范数意义下的变差及相互关系;借助于广义算子的Wick积运算,引入了广义算子值函数关于广义算子值测度的一种积分一Bochner-Wick积分,讨论了这种积分的性质,建立了相应的收敛定理并且展示了其在量子白噪声理论中的应用;探讨了Bochner.-Wick积分的Fubini定理及相关问题.Generalized operators of white noise play a very important role in the theory and application of white noise analysis. In the present thesis, we mainly discuss the integration of generalized operatorvalued functions with respect to generalized operator-valued measures and related topics. The main work is as follows： First, a notion of generalized operator-valued measures is introduced, and variations of such a measure are investigated in the sense of symbol and operator p-norm, respectively. Secondly, an integral, called Bochner-Wick integral, of a generalized operator valued function with respect to a generalized op- erator valued measure is defined. Properties of the integral are examined and corresponding convergence theorems are established. Finally, the Yhbini theorem for the integral is discussed and applications are shown.

关 键 词：白噪声空间 广义算子值函数 象征 Bochner-Wick积分. 

分 类 号：O211.63[理学—概率论与数理统计]