Particle Transport Operator and it’s Semi-group at Lebesgue Skale

Spectrums of particles transport operator (and it’s semi-group) which describes their motion and adsorption (without generation) in linearized Boltzmann equation is investigated in this paper. Together with corresponding initial and boundary conditions this equation describes many processes of particle transport (from neutrons and photons in nuclear reactors and star’s atmospheres correspondingly till cells in growing populations and texts in libraries).