On the Spectrum of a One-Velocity Transport Operator with Maxwell Boundary Condition*

The spectrum of a one-velocity transport operator with Maxwell boundary condition is discussed in L1 space. First, it is proved that the spectrum of a streaming operator associated with the transport operator consists of infinitely isolated eigenvalues, each of which is simple; furthermore, a formula for computation of these eigenvalues is obtained. Second, it is proved that the essential spectrum of the transport operator is empty and it is pointed out that the dominant eigenvalue of the transport operator exists. Finally, a necessary and sufficient condition for the existence of a complex eigenvalue of the transport operator in a right half plane is given.