Characterization Theorems for the Quantum White Noise Gross Laplacian and Applications

摘要

This paper reports on the characterization of the quantum white noise (QWN) Gross Laplacian based on nuclear algebra of white noise operators acting on spaces of entire functions with.-exponential growth of minimal type. First, we use extended techniques of rotation invariance operators, the commutation relations with respect to the QWN-derivatives and the QWN-conservation operator. Second, we employ the new concept of QWN-convolution operators. As application, we study and characterize the powers of the QWN-Gross Laplacian. As for their associated Cauchy problem it is solved using a QWN-convolution and Wick calculus.