Bounds for the continuation of perturbative results to the spectral region

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Abstract
The problem of analytic continuation to the boundary of the holomorphy domain from both continuous and discrete interior sets has recently been the subject of detailed analyses. This problem is important in phenomenological applications but is also of interest in theoretical calculations, e.g., in attempting to evaluate the parameters of resonances or other nonperturbative effects in QCD. Because of the inherent instability of the continuation problem it is necessary to introduce additional criteria—which should be physically based—to select the right continuation function. In this paper, the results thus obtained for continuation from a continuum are examined for stability, and bounds are derived for the errors on the boundary in terms of the uncertainty of the input data. The procedure is shown to be stable in the sense that these bounds tend to zero as the data errors go to zero.