Integral equations of the first kind in problems of wave scattering in hollow wave guides

The problem of wave scattering by foreign inclusions in hollow wave guides is reduced to an integral Fredholm equation of the first kind with a regular kernel over the surface of the inclusion, which is expressed in terms of the Green's function of the empty system. The uniqueness of the solution of this equation is proved. Various types of inclusions are considered: good conductors, dielectrics, and inhomogeneous objects.