Extensions of the derivative dispersion relations for amplitude analyses

It is shown that analyticity properties of scattering amplitudes as expressed by the derivative analyticity relations can be combined with measured cross-section and polarization data to extract the full scattering amplitudes in a simple and practical way. The method should be particularly useful in problems involving a coupled amplitude analysis. The measurement of a complete set of spin parameters, or a phase-shift analysis at only one energy, is sufficient to eliminate ambiguities in the extraction at all other energies. Our procedure is illustrated by considering both simple mathematical examples and real data