The point spectrum of the linearized Boltzmann operator with an external potential in an unbounded domain

We will investigate the point spectrum on the imaginary axis of the lineari zed Boltzmann operator with an external-force potential in an unbounded dom ain. The boundary condition considered is the perfectly reflective boundary condition. We suppose that the boundary surface is sufficiently smooth, bu t is not cylindrical. In this case, the point spectrum on the imaginary axi s is only equal to {0}.