  We present three novel forms of the Monge-Ampere equation, which is used,
e.g., in image processing and in reconstruction of mass transportation in the
primordial Universe. The central role in this paper is played by our Fourier
integral form, for which we establish positivity and sharp bound properties of
the kernels. This is the basis for the development of a new method for solving
numerically the space-periodic Monge-Ampere problem in an odd-dimensional
space. Convergence is illustrated for a test problem of cosmological type, in
which a Gaussian distribution of matter is assumed in each localised object,
and the right-hand side of the Monge-Ampere equation is a sum of such
distributions.
