Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1

We consider the abstract scattering structure of the non homogeneous linearized Vlasov-Poisson equations from the viewpoint of trace class properties which are emblematic of the abstract scattering theory [13, 14, 15, 19]. In dimension 1+1, we derive an original reformulation which is trace class. It yields the existence of the Moller wave operators. The non homogeneous background electric field is periodic with 4 + epsilon bounded derivatives.