On the theory of brownian motion

The spectrum of the Fokker-Planck operator for weakly coupled gases is considered. The operator is decomposed into operators acting on functions whose angular dependence is given by spherical harmonics. It is shown that the operator corresponding to l = 0 has zero for a point eigenvalue (the eigenfunction is the Maxwell distribution). There are no other point eigenvalues and the continuous spectrum of all of the operators is the entire negative real axis. Some consequences are briefly discussed.