On the necessity of nearly-best-possible methods for analytic continuation of scattering data

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Abstract
In the present paper we discuss some mathematical methods which are nearly-best-possible in order to extract as much as possible information from the numerical analytic continuation of the scattering data. All the questions related to the stability are analyzed; in this sense we explicitly show some cases where the continuity of the solutions on the data is very poor. Finally the error-bounds are extensively explored.