Generalizing Caratheodory's uniqueness of harmonic parameterization to N dimensions

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