Wick differential and Poisson equations associated to the e???e???e???-Euler operator acting on generalized operators

摘要

In this paper we study the homogeneous Wick differential equation associated to the quantum white noise (e???e???e???) Euler operator ??Eg,Q acting on generalized operators. ??Eg,Q is defined as sum of the extension of the e???e???e???-Gross Laplacian and the e???e???e???-conservation operator. It is shown that the operator ??Eg,Q has a representation in terms of the e???e???e???-derivatives {Dca??,Dc+:ca??N}. The poisson equation is worked out as a non homogeneous Wick differential equation associated to ??Eg,Q.