Koopman and Perron-Frobenius operators on reproducing kernel Banach spaces.

Koopman and Perron-Frobenius operators for dynamical systems are becoming popular in a number of fields in science recently. Properties of the Koopman operator essentially depend on the choice of function spaces where it acts. Particularly, the case of reproducing kernel Hilbert spaces (RKHSs) is drawing increasing attention in data science.