Volume singular integral equation method in electromagnetic theory

We consider volume singular integral equations which describe the problems of electromagnetic scattering from three-dimensional anisotropic media characterized by permittivity and permeability. We performed a detailed analysis of these equations and corresponding scattering problems, including nonclassical ones. We consider the equivalence of the boundary value problems for the Maxwell equations and the singular integral equations and formulate the corresponding theorem. We obtain the necessary and sufficient conditions that provide the fulfillment of the Noether property of the operator and sufficient conditions for the Fredholm property. We prove the existence and uniqueness theorems for a very wide family scattering problems.