Analytic characteristics of time-correlation functions

It is shown how the analytic properties of classical equilibrium time-autocorrelation functions (TACF's) and the corresponding memory functions (MF's), associated with the generalized Langevin equation in the Schmidt-orthogonalized representation, are intimately connected. In particular, the Maclaurin expansions of the TACF and Schmidt MF's and the continued-fraction representations of the corresponding Laplace transforms exist and converge in well-defined domains and under conditions consistent with the existence of finite positive transport coefficients.