Positivity and unimodality as stabilizers of the analytic extrapolation of a function known with errors

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Abstract
Positivity and unimodality hypotheses on an unknown function χ1(x) confer Stieltjes character to another function H1(z), known in a discrete set of real points and affected by errors caused by experimental measurements, and impose constraints on the coefficients of its formal expansion which limit the universe of approximant functions, so acting as stabilizers of the analytic extrapolation. The type I Padé approximants, built with the coefficients of the formal expansion, provide rigorous bounds on the function in the cut complex plane. The application of a Stieltjes–Chebyshev technique allows approximations to the function, even on the cut, to be obtained. The physical problem of K±p forward elastic scattering is approached by the previous method, and bounds on the coupling constant and real part of the amplitude are found.