白噪声分析中广义算子值函数的Bochner-Wick积分

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---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.

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

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 operator-valued 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 operator valued measure is defined. Properties of the integral are examined and corresponding convergence theorems are established. Finally, the Fubini theorem for the integral is discussed and applications are shown.