Moment Characterization Of Generalized Operators And Its Applications

In this paper, we use the moment approach to discuss generalized operators and its applications. Firstly, we give a definition of vector-valued moment to a generalized operator and discuss the characterization of generalized operators in terms of their vector-valued moments on Kubo framework of white noise analysis. Several moment characterization theorems are established. Secondly, we use these moment characterization theorems to discuss the convergence of sequences of generalized operators and the integral of functions of generalized operator-valued on Kubo framework of white noise analysis. Finally, we extend our main results to Kondratiev-Streit framework of white noise analysis.