The mathematical problem of unique recovery of a band-limited multidimensional signal from its phase or its magnitude is considered. Specifically, it is shown that any irreducible band-limited function f(s//1,. . . ,s//n), S//i an element of C, i equals 1,. . . , n is uniquely determined, except for trivial associates, from (1) the phase of f(x//1,. . . , x//n), x//i an element of R, i equals 1,. . . , n, if not all the zeros of f(s//1,. . . ,s//n) occur in conjugate pairs; or (2) the magnitude of f(x//1,. . . ,x//n) x//i an element of R, i equals . . . , n.
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