Convolution theorem for non-degenerate maps and composite singularities

We give a formula for the spectral pairs (after Steenbrink) for composite singularities of several variables. (Note that for two variable case is studyed by Nemethi-Steenbrink.) Here composite singularity is given by the equation f(g_1, …, g_n) = 0. For technical reason, we assume that f is non-degenerated with respect to the Newton boundary.