Treatment of the periodically inhomogeneous surface: multiple boundary condition

We deal with the following question: how can the composite nature of a boun dary condition formulated for a periodically inhomogeneous surface and invo lving the composite surface parameter, be treated analytically? We show tha t when the appropriate Fourier transformation is applied, the composite bou ndary condition reduces to a specific eigenproblem condition, which constit utes the spectrum of eigenvalues of an "effective" surface parameter, a nov el quantity we introduced to account for the nonhomogeneity of the surface.