Approximating Koopman and Perron-Frobenius Operators from Data: Convergence Rates and Error Bounds

This work introduces a unified framework for data-driven approximation of linear operators associated with dynamical systems, such as the Koopman and Perron-Frobenius operators and their generators. The authors prove convergence of the approximations to the true operators under minimal assumptions, and derive explicit convergence rates and error bounds, accounting for the presence of noise in the observations.