THE SOLUTION OF BOUNDARY-VALUE-PROBLEMS FOR THE EQUATIONS OF RADIATION TRANSFER

The theory of the solution of half-space boundary-value problems and the vector equations of radiation transfer describing the scattering of polarized light is constructed. Separation of the variables leads to a characteristic equation for which the spectrum of eigenvalues is investigated and eigenvectors are found in the space of generalized functions. A theorem on the expansion of the solution in terms of eigenvectors of discrete and continuous spectra is proved. The proof reduces to solving the Riemann-Hilbert vector boundary-value problem with a matrix coefficient. After diagonalization and factorization of the coefficient, a solution of the boundary-value problem in the class of meromorphic vectors is given. The solvability conditions allow a unique determination of the unknown coefficients of the expansion and the free parameters of the solution.