Generalizing Caratheodory's uniqueness of harmonic parameterization to N dimensions

Consider a sum of F exponentials in N dimensions, and let I, be the number of equispaced samples taken along the nth dimension. it is shown that if th e frequencies or decays along every dimension are distinct N and Sigma (N)( n=1) I-n greater than or equal to 2F + (N - 1), then the parameterization i n terms of frequencies, decays, amplitudes, and phases is unique. The resul t can be viewed as generalizing a classic result of Caratheodory to N dimen sions. The proof relies on a recent result regarding the uniqueness of low- rank decomposition of N-way arrays.