L2-synthesis by ambiguity functions

A class of operators on L 2 (R 2) are introduced which, when acting on rank-one tensors, yield ambiguity functions and their generalizations. The L 2 — synthesis problem by functions in the range of these operators is solved. The same approach applied to functions whose Fourier transforms are rank-one tensors yields analogous results for wideba.nd ambiguity functions (wavelet transforms).