A framework for coherent pattern extraction and prediction of observables measure-preserving, ergodic dynamical systems with both atomic continuous spectral components is developed. This based on an approximation the generator system by a compact operator Wτ reproducing kernel Hilbert space (RKHS). The skew-adjoint, thus can be represented projection-valued measure, discrete compactness, associ...

We demonstrate that a reproducing kernel Hilbert space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.