Eigendecompositions of transfer operators in reproducing kernel Hilbert spaces

DOI10.1007/s00332-019-09574-zzbMath1437.37104arXiv1712.01572OpenAlexW2775659970WikidataQ127340873 ScholiaQ127340873MaRDI QIDQ2303767

Krikamol Muandet, Stefan Klus, Ingmar Schuster

Publication date: 5 March 2020

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01572

zbMATH Keywords

Perron-Frobenius operatorKoopman operatoreigendecompositionskernel Hilbert spaceskernel mean embeddings

Mathematics Subject Classification ID

Time series analysis of dynamical systems (37M10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

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Cites Work

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• A kernel-based method for data-driven Koopman spectral analysis
• On the numerical approximation of the Perron-Frobenius and Koopman operator
• Data-driven model reduction and transfer operator approximation
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• Kernel methods in machine learning
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• Rates of convergence for everywhere-positive Markov chains
• Transition manifolds of complex metastable systems. Theory and data-driven computation of effective dynamics
• On convergence of extended dynamic mode decomposition to the Koopman operator
• Reproducing kernel Hilbert space compactification of unitary evolution groups
• On dynamic mode decomposition: theory and applications
• Hilbert space embeddings and metrics on probability measures
• 10.1162/153244303768966085
• Dynamic mode decomposition of numerical and experimental data
• Support Vector Machines
• A Hilbert Space Embedding for Distributions
• Spectral analysis of nonlinear flows
• Joint Measures and Cross-Covariance Operators
• Kernel Mean Embedding of Distributions: A Review and Beyond
• 10.1162/153244302760200687
• A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
• Mutual Information for Gaussian Processes