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Article Dans Une Revue Chaos: An Interdisciplinary Journal of Nonlinear Science Année : 2022

Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces

Résumé

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. 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.

Dates et versions

hal-04174199 , version 1 (31-07-2023)

Identifiants

Citer

Masahiro Ikeda, Isao Ishikawa, Corbinian Schlosser. Koopman and Perron–Frobenius operators on reproducing kernel Banach spaces. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32 (12), pp.123143. ⟨10.1063/5.0094889⟩. ⟨hal-04174199⟩
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