SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 232-261, January 2021.
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 CFL condition of finite difference schemes for advection equations. Numerical results of spectral computations are shown for some benchmark examples of volume-preserving flows.

中文翻译：

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保测流的考夫曼谱的逼近

SIAM应用动力系统杂志，第20卷，第1期，第232-261页，2021年1月。
使用周期逼近来计算Koopman算子的频谱分解的方法被推广到紧凑度量空间上的保度量流类。结果表明，连续一参数unit群的频谱分解可以从流的中间时间离散化近似得出。在流的时间离散化与周期逼近的空间离散化之间建立了充分的条件，从而在极限范围内将发生光谱的弱收敛。这种情况有效地转化为以下要求：空间细化必须比时间细化更快。将该结果与对流方程的有限差分格式的众所周知的CFL条件进行了对比。