The Numerical Approximation of Koopman Modes of a Nonlinear Operator Along a Trajectory

The spectral theory of linear operators enables the analysis of their properties on stable subspaces. The Koopman operator allows to extend these approaches to a large class of nonlinear operators in a surprising way. This is even applicable for numerical analysis of time dependent data of simulations and measurements. We give here some remarks on the numerical approach, link it to spectral analysis by the Herglotz-Bochner theorem and are doing some steps for significance for partial differential equations.