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We study the degree of reliability of extrapolation of complexelectromagnetic permittivity functions based on their analyticity properties.Given two analytic functions, representing extrapolants of the sameexperimental data, we examine how much they can differ at an extrapolationpoint outside of the experimentally accessible frequency band. We give a sharpupper bound on the worst case extrapolation error, in terms of a solution of anintegral equation of Fredholm type. We conjecture and give numerical evidencethat this bound exhibits a power law precision deterioration as one movesfurther away from the frequency band containing measurement data.

On feasibility of extrapolation of the complex electromagnetic permittivity function using Kramer-Kronig relations