On holomorphic extrapolations of the scattering amplitude into the complex plane

Dispersion-relation extrapolations of the scatering amplitude compatible with error affected data are discussed. It is shown that if the complex argument z is chosen so that the analyticity domain D of the amplitude is the interior of the unit circle the Cauchy kernel 1/(z'-z) gives the best holomorphic extrapolation linear in the data input in the sense that its error bounds cannot be improved simultaneously for all points of D.