  Reconstruction of density functions and their characteristic functions by
radial basis functions with scattered data points is a popular topic in the
theory of pricing of basket options. Such functions are usually entire or admit
an analytic extension into an appropriate tube and "bell-shaped" with rapidly
decaying tails. Unfortunately, the domain of such functions is not compact
which creates various technical difficulties. We solve interpolation problem on
an infinite rectangular grid for a wide range of kernel functions and calculate
explicitly their Fourier transform to obtain representations for the respective
density functions.
