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.