Koopman Operator Framework for Spectral Analysis and Identification of Infinite-Dimensional Systems

We consider the Koopman operator theory in context of nonlinear infinite-dimensional systems, where is defined over a space bounded continuous functionals. The properties semigroup are described and finite-dimensional projection proposed, which provides linear approximation underlying dynamics. This used to obtain spectral from data, method can be seen as generalization Extended Dynamic Mode Decomposition for systems. Finally, we exploit proposed framework identify (a of) Lie generator associated with semigroup. approach yields PDE identification, complemented theoretical convergence results.