Duality, Green's functions and all that

Abstract

The basic duality relation between the direct and adjoint linear transport operators is analyzed and used to derive a duality relation between the direct and adjoint Green's functions with general albedo conditions. Convolution relations are derived for Green's functions defined on domains with non empty intersection. The duality framework is used to derive known results such as the reciprocity theorem, integrals equations and Placzek's lemma with applications to the construction of Green's functions with factored albedos and boundary perturbation problems. A new equation for the source function is also given.