20 citations · 41 across the 20 of their papers we have counts for
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A Data-Driven Framework for Koopman Semigroup Estimation in Stochastic Dynamical Systems
Yuanchao Xu, Kaidi Shao, Isao Ishikawa +3
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing meth…
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda +1
This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what…
Koopman spectral analysis of skew-product dynamics on Hilbert -modules
Dimitrios Giannakis, Yuka Hashimoto, Masahiro Ikeda +2
We introduce a linear operator on a Hilbert -module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it ad…
Generalized eigenvalues of the Perron-Frobenius operators of symbolic dynamical systems
Hayato Chiba, Masahiro Ikeda, Isao Ishikawa
The generalized spectral theory is an effective approach to analyze a linear operator on a Hilbert space with a continuous spectrum. The generalized spectrum is compu…