Separability and axial symmetry of M-D polynomials and maximum-entropy M-D random Processes

In multidimensional system and signal analysis it is often assumed that an M-dimensional (M-D) polynomial is separable. The following properties are presented to show rationales of the separability assumption. First, if an M-D polynomial is separable, it is axially symmetric. Second, if the autocorrelation generating function of an M-D deterministic sequence with the support in the first 2^M-rant is axially symmetric, it is separable. Third, if a wide-sense stationary and 2^M-rant causal M-D stochastic process has the maximum entropy subject to marginal autocovariance constraints, it is separable.