Relaxation rate distribution from frequency or time dependent data

A method for the inversion of experimental susceptibility spectra or relaxation functions in terms of a spectrum of relaxation times is proposed. The method uses the Boas–Widder formula for the inversion of the Laplace transform for real variables. The method is tested numerically on known spectra for the Cole–Cole, Cole–Davidsson and Kohlrausch–Williams–Watts models as well as for more complex spectra obtained from the mode-coupling theory, and in all cases the agreement is very good.