  The method of using periodic approximations to compute the spectral
decomposition of the Koop- man operator is generalized to the class of
measure-preserving flows on compact metric spaces. It is shown that the
spectral decomposition of the continuous one-parameter unitary group can be
approximated from an intermediate time discretization of the flow. A sufficient
condition is established between the time-discretization of the flow and the
spatial discretization of the periodic approximation, so that weak convergence
of spectra will occur in the limit. This condition effectively translates to
the requirement that the spatial refinements must occur at a faster pace than
the temporal refinements. This result is contrasted with the well-known CLF
condition of finite difference schemes for advection equations. Numerical
results of spectral computations are shown for some benchmark examples of
volume-preserving flows.
