On Half-Range Expansion Theorems in Studies of Polarized Light

摘要

The established normal modes of the vector equation of transfer describing the transport of polarized light are used to construct solutions to typical half-space problems. The half-range completeness theorem required by this method is discussed in the context of systems of singular integral equations. Although the Riemann-Hilbert problem encountered here is defined in terms of continuous rather than Holder continuous functions, the existence of a canonical solution is established, and the developed properties of this canonical matrix are used to complete the proof of the necessary half-range expansion theorem. (Author)