Spectrum of the transport operator in a nonuniform slab with generalized boundary conditions

Spectral properties of the transport operator in a nonuniform slab with generalized boundary conditions were first studied in Ref. [1]. The author showed that the operator is an infinitesimal generator of a C-0-semigroup and it has at least one real eigenvalue displaying the asymptotic behavior of the initial-value problem. Both continuous spectrum and possible accumulation points of isolated eigenvalues have not been considered. In this paper, we show that the continuous spectrum fill in a passage, and the possible accumulation points of isolated eigenvalues in the right half plane lie on the right boundary of the passage.