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

Estimates of solutions of linear Boltzmann equation at large time and spectral singularities