Paley–Wiener criterion for relaxation functions

The conclusion [K. L. Ngai, A. K. Rajagopal, R. W. Rendell, and S. Teitler, Phys. Rev. B 28, 6073 (1983)] that simple exponential decay is a nonviable model for electrical relaxation, because it fails to satisfy the fundamental Paley–Wiener Fourier transform criterion, is shown by direct analysis to be inapplicable to small-signal electrical relaxation situations. Thus, not only is exponential decay and its associated single-relaxation-time Debye frequency response a valid model for relaxation, but, by extension, all distributions of relaxations times and energies which use a superposition of simple exponentials or Debye functions are also acceptable descriptions of relaxation phenomena. Reasons why the earlier conclusion is nonviable in the present context are discussed.