We discuss the use of rational approximants in the performance of stable analytic extrapolation from interior points of the analyticity domain to other interior. points. We show that the instability of analytic extrapolation and the presence of nOIse sets an upper bound to the number of parameters that can be used in the soluti~n. We generalize this result to other classes of functions which are used to fit expenmental data and present a number of practical examples in form factor analysis.
It is shown that the problem of the construction of scattering amplitudes with Mandelstam analyticity from knowledge of their modulus in the three physical channels can be reduced, within a rather large class of functions, to the second Cousin problem of the theory of functions of two complex variables. As a consequence, it can be solved completely and explicitly. We derive conditions on the modulus function, under which at least one solution exists, as well as criteria for the correct resolution of the discrete ambiguity at fixed energy.
The paper contains a discussion of the phase retrieval problem in two dimensions and proposes criteria to select those resolutions of the discrete ambiguity of the zero trajectories which are compatible with the analyticity in two variables of the scattered field.
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