  Extended dynamic mode decomposition (EDMD) provides a class of algorithms to
identify patterns and effective degrees of freedom in complex dynamical
systems. We show that the modes identified by EDMD correspond to those of
compact Perron-Frobenius and Koopman operators defined on suitable
Hardy-Hilbert spaces when the method is applied to classes of analytic maps.
Our findings elucidate the interpretation of the spectra obtained by EDMD for
complex dynamical systems. We illustrate our results by numerical simulations
for analytic maps.
