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.