The spectrum of the transport operator with a potential term under the spatial periodicity condition (Q1373408)

The authors are concerned with the transport operator with a potential term and the spatial periodicity condition, from which follows that the transport operator is essentially the same as that in the 3-dimensional torus. The main result is that there exists a positive constant \(C\) such that, for each \(\Theta \in [0,1)\), the intersection of \(\{\mu\in \mathbb{C}\mid \text{Re} \mu> -\Theta C\}\) and the spectrum of the transport operator is a finite set which consists only of eigenvalues of the transport operator with finite (algebraic) multiplicity.