Use of the continuous spectrum in the method of partial regions

In the internal problems of electrodynamics, solved by the method of partial regions, in the case where at least one of the selected partial regions cannot be formulated boundary value problem of Sturm-Liouville problem, the introduction of a continuous spectrum of eigenfunctions is required. Strictly speaking, the functions in this range, you should not call their own, because they are not solutions of the homogeneous boundary value problem. Therefore, the classification used to be considered a conditional: these functions are solutions of the semi-homogeneous boundary value problem - the problem on the homogeneous Helmholtz equation with a partially open boundary. Problems with partially or completely open borders require recording solutions as an integral in the spectral region.