Linear Boltzmann Operator and it’s Semi-group at Lebesgue Scale

The spectrum of linear Boltzmann operator (and it’s semi-group) which describes processes of particles transport and their adsorption with 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).