Determination of Thermodynamic Green's Functions

In the study of thermodynamic correlation functions or Green's functions, one is naturally led to a calculation of values of the Fourier transform of the Green's function on a discrete set of points in the complex energy plane. It is shown that even though these points do not in general possess a limit point within the region of analyticity, one may still uniquely determine the Fourier transform of the Green's function directly from its values at these points.