Justification of integral representations for fields in a diffraction problem on a cluster of particles in a plane-layered medium (Q656492)

The work is devoted to the study of an electromagnetic field diffraction problem on a cluster of permeable particles placed in a plane-layered medium. For obtaining a mathematical justification of the integral field representations constructed on the basis of the discrete source method, two theorems are presented. The first shows the completeness and closedness of the corresponding system of basis functions and the second -- as a direct consequence of the first -- the convergence of the approximate solution to the exact solution of the original electromagnetic wave diffraction boundary value problem.