Abstract
This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L 1-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C 0-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given. [PUBLICATION ABSTRACT]