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

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