Abstract
The chapter discusses the analysis of complete and linear independent systems of functions for the Maxwell equations. The analysis begins by presenting some fundamental results on the completeness of the localized spherical vector wave functions. The completeness properties of the systems of discrete sources are of primary interest as they provide a means for approximating the exact solutions to the scattering problems. To preserve the completeness at irregular frequencies, linear combinations of these functions are considered. Next, the completeness properties of the systems of distributed sources are analyzed. The analysis is based on the addition theorem for spherical wave and vector wave functions. The next section of the chapter is concerned with the completeness of the system of vector Mie potentials with singularities distributed on auxiliary closed and open surfaces. These functions are suitable for analyzing the scattering by particles without rotational symmetry. The last section of this chapter deals with the linear independence of these systems.
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