  The Koopman operator induced by a dynamical system is inherently linear and
provides an alternate method of studying many properties of the system,
including attractor reconstruction and forecasting. Koopman eigenfunctions
represent the non-mixing component of the dynamics. They factor the dynamics,
which can be chaotic, into quasiperiodic rotations on tori. Here, we describe a
method through which these eigenfunctions can be obtained from a kernel
integral operator, which also annihilates the continuous spectrum. We show that
incorporating a large number of delay coordinates in constructing the kernel of
that operator results, in the limit of infinitely many delays, in the creation
of a map into the discrete spectrum subspace of the Koopman operator. This
enables efficient approximation of Koopman eigenfunctions from high-dimensional
data in systems with pure point or mixed spectra.
