  The spectral analysis of the dissipative linear transport (Boltzmann)
operator with polynomial collision integral by the Szokefalvi-Nagy - Foias
functional model is given. An exact estimate for the reminder in the asymptotic
of the corresponding evolution semigroup is proved in the isotropic case. In
the general case, it is shown that the operator has finitely many eigenvalues
and spectral singularities and an absolutely continuous essential spectrum, and
an upper estimate for the reminder is established.
