Spectral analysis of the transport operator: A functional model approach

This paper presents the spectral analysis of the dissipative one-speed transport operator for the cases of a finite slab and of a finite body, by means of the Szokefalvi-Nagy - Foias functional model. It is shown that the essential spectrum of the operator is absolutely continuous with one possible spectral singularity at point 0. The absolutely continuous component of the operator is studied in detail in the nontrivial case, when the spectral singularity does occur.