Formulation and generality of the one-wavelength analytic continuation principle

Formulate precisely and prove general conditions under which the one-wavelength principle for rational-function-based analytic continuation holds, quantifying its dependence on approximation accuracy and problem class.

Background

The authors observe empirically that AAA-based analytic continuation often succeeds for roughly one wavelength beyond the data domain at default precision, and about two wavelengths at higher precision. They explicitly state uncertainty regarding its generality and precise formulation. A rigorous description would guide practical continuation strategies and inform error control.