# The kernel perspective on dynamic mode decomposition

arXiv: https://arxiv.org/abs/2106.00106 · HTML: https://mlsanity.com/paper/2106.00106/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 34 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 4 of 4)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator](https://mlsanity.com/paper/1703.04680/) (2017)
- [Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions](https://mlsanity.com/paper/1911.11992/) (2019)

## Built on by (most cited first, 3 of 3)

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Fast dynamical similarity analysis](https://mlsanity.com/paper/2511.22828/) (2025)
- [Integral Formulation of QENDy for Robust Nonlinear System Identification](https://mlsanity.com/paper/2606.11629/) (2026)

## Abstract (arXiv)

This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eigenfunctions between Koopman operators, and boundedness and compactness of Koopman operators. Counterexamples that illustrate restrictiveness of the assumptions are provided for each of the assumptions. In particular, this manuscript proves that the native reproducing kernel Hilbert space (RKHS) of the Gaussian RBF kernel function only supports bounded Koopman operators if the dynamics are affine. In addition, a new framework for DMD, that requires only densely defined Koopman operators over RKHSs is introduced, and its effectiveness is demonstrated through numerical examples.