Infinite-snapshot limit of functional DMD

Determine what happens to projected functional DMD and exact functional DMD in the limit of an infinite number of snapshots.

Background

The paper develops projected functional DMD and exact functional DMD for learning finite-rank operators associated with infinite-dimensional dynamical systems from functional snapshots. After discussing possible convergence of classical DMD as the spatial discretization becomes arbitrarily fine, the conclusion identifies the corresponding asymptotic behavior as the number of training snapshots tends to infinity as unresolved. The question concerns the limiting behavior and, implicitly, convergence properties of the proposed functional DMD methods when increasingly many snapshots are available.