Functional investigation and kernel expansion technique for the system of integral equations governing the stationary anisotropic transport of monoenergetic neutrons in threedimensional media

Starting from the third form of the stationary Boltzmann transport equation for monoenergetic neutrons we get a system of linear integral equations for the expansion coefficients of the neutron angular flux in a spherical harmonics series. Such a system is then studied by extensively using methods of functional analysis, and many mathematical properties of the unknown flux distribution are recognized ''a priori''. This gives rise to a rigorous constructive technique for solving the system of integral equations, on the basis of a suitable decomposition of its kernels