Paley-Wiener criterion for relaxation functions

Abstract

It is shown how the Paley-Wiener theorem in Fourier-transform theory can provide the bound for physically acceptable relaxation functions for long times. In principle the linear exponential decay function, and hence also a superposition of linear exponential decay functions, does not provide an acceptable description of relaxation phenomenon although the Paley-Wiener bound can be made to approach arbitrarily close to linear exponential. A class of relaxation functions proposed recently obeys the Paley-Wiener bound. The general necessity for time-dependent relaxation rates is emphasized and discussed.