Bridging Koopman Operator and time-series auto-correlation based Hilbert-Schmidt operator

Yicun Zhen, Bertrand Chapron, Etienne Mémin

Given a stationary continuous-time process $f(t)$, the Hilbert-Schmidt operator $A_{\tau }$ can be defined for every finite $\tau$\cite{Vautard1989SingularSA}. Let ${\lambda }_{\tau ,i}$ be the eigenval…