Koopman and Perron-Frobenius Operators on reproducing kernel Banach spaces

Abstract

Koopman and Perron-Frobenius operators for dynamical systems have been getting popular in a number of fields in science these days. 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) draws more and more attention in data science. In this paper, we give a general framework for Koopman and Perron-Frobenius operators on reproducing kernel Banach spaces (RKBSs). More precisely, we extend basic known properties of these operators from RKHSs to RKBSs and state new results, including symmetry and sparsity concepts, on these operators on RKBS for discrete and continuous time systems.

We add a reference and correct some typos

References in corpus (3)

• Applied Koopmanism
• On $L^2$ -functions with bounded spectrum
• Composition operators on Sobolev spaces, $Q$-mappings and weighted Sobolev inequalities

Cited by in corpus (4)

• Consistent spectral approximation of Koopman operators using resolvent compactification
• Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
• Koopman and transfer operator techniques from the perspective of quantum theory
• Boundedness of composition operator in Orlicz-Morrey spaces