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Paper Citation Record · LEDGER

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition

As of 17 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:1909.01419.

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pith.paper-citation-record.v1
1909.01419 v4

Coverage vector

measured 54 of 54 reference resolution

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measured 54 of 54 standing notices

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

54 of 54 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bbb0b4ad-a223-4412-9e67-005ce1c7a364 · outbound

This paper cites Efficient identification of linear evolutions in nonlinear vector fields: Koopman invariant subspaces,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Efficient identification of linear evolutions in nonlinear vector fields: Koopman invariant subspaces,

Reference 1

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verified fuzzy
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation b9f93d93-95cf-40ae-9897-73a0057a4a77 · outbound

This paper cites Hamiltonian systems and transformation in Hilbert space,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Hamiltonian systems and transformation in Hilbert space,

Reference 2

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Observation 754be019-84f4-4f82-9444-e28921c5f6f7 · outbound

This paper cites Dynamical systems of continuous spectra,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Dynamical systems of continuous spectra,

Reference 3

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Observation 2af62975-0f32-49fd-9b25-c8c86cf63995 · outbound

This paper cites Spectral properties of dynamical systems, model reduction and decompositions,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Spectral properties of dynamical systems, model reduction and decompositions,

Reference 4

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verified fuzzy
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Observation f83c9d89-e3ba-4299-b316-ae24803d01b1 · outbound

This paper cites Spectral analysis of nonlinear flows,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Spectral analysis of nonlinear flows,

Reference 5

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 31610b87-072a-4e2c-8781-1f840524e0e3 · outbound

This paper cites Applied Koopmanism,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Applied Koopmanism,

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 8c6d8172-eb50-4c08-a8ac-013f09c1ca9f · outbound

This paper cites Koopman operator framework for constrained state estimation,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Koopman operator framework for constrained state estimation,

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation d984d801-b3b5-4ea6-b3a2-32a7cdbae1ba · outbound

This paper cites A robust data-driven Koopman Kalman filter for power systems dynamic state estimation,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition A robust data-driven Koopman Kalman filter for power systems dynamic state estimation,

Reference 8

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 1f77ab34-1cfd-4f87-ae9b-32c14b6fd554 · outbound

This paper cites Koopman-based lifting techniques for nonlinear systems identification,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Koopman-based lifting techniques for nonlinear systems identification,

Reference 9

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation a9414e26-d3be-4e10-af84-31c13ec904b3 · outbound

This paper cites Nonlinear system identifi- cation of soft robot dynamics using Koopman operator theory,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Nonlinear system identifi- cation of soft robot dynamics using Koopman operator theory,

Reference 10

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation c234d220-5178-41a9-86dc-3eb8d8eee75a · outbound

This paper cites Sparse sensing and DMD-based identification of flow regimes and bifurcations in complex flows,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Sparse sensing and DMD-based identification of flow regimes and bifurcations in complex flows,

Reference 11

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verified fuzzy
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Source-reported events for the cited work

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Observation 9517698a-ef90-4ceb-8e74-fec72267cf5d · outbound

This paper cites Operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics,

Reference 12

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation cad837be-2cef-45e9-9797-f429530fbc30 · outbound

This paper cites Data-driven model reduction and transfer operator approximation,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Data-driven model reduction and transfer operator approximation,

Reference 13

Resolution
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Observation c7f21603-3e24-4313-a940-9881f28b7f2a · outbound

This paper cites Nonlinear model order reduction via dynamic mode decomposition,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Nonlinear model order reduction via dynamic mode decomposition,

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 81af22cf-96cf-49e7-9ee5-e512dbe3c8eb · outbound

This paper cites Linear predictors for nonlinear dynamical sys- tems: Koopman operator meets model predictive control,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Linear predictors for nonlinear dynamical sys- tems: Koopman operator meets model predictive control,

Reference 15

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Source-reported events for the cited work

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Observation a0984e01-96b9-44c0-9c65-4e7c25438440 · outbound

This paper cites A data-driven Koopman model predictive control framework for nonlinear flows.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition A data-driven Koopman model predictive control framework for nonlinear flows

Reference 16

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 72522e86-2743-434b-bdbc-fd912e61d642 · outbound

This paper cites Koopman operator-based model reduction for switched-system control of PDEs,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Koopman operator-based model reduction for switched-system control of PDEs,

Reference 17

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation d0d00d0d-2bcb-47e8-8a79-dcfe94fb2470 · outbound

This paper cites Feedback stabilization using Koop- man operator,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Feedback stabilization using Koop- man operator,

Reference 18

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 48c7657a-a5bc-4076-863f-2ce75441d7e8 · outbound

This paper cites Data-driven discovery of Koopman eigenfunctions for control.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Data-driven discovery of Koopman eigenfunctions for control

Reference 19

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 34e2bf48-6d4f-4de3-ba21-b3f44cefbbad · outbound

This paper cites Pulse-based control using Koopman operator under parametric uncertainty,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Pulse-based control using Koopman operator under parametric uncertainty,

Reference 20

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 4f2c70d5-d039-44bc-89e5-50d1f4dea8b0 · outbound

This paper cites Data-driven feedback stabilization of nonlinear systems: Koopman-based model predictive control.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Data-driven feedback stabilization of nonlinear systems: Koopman-based model predictive control

Reference 21

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verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 87cab151-dc64-4ae6-8f5c-0ecc8b6cbcf9 · outbound

This paper cites Local Koopman operators for data-driven control of robotic systems,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Local Koopman operators for data-driven control of robotic systems,

Reference 22

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 3f7ac862-2e19-43f2-8b32-599ea7c4ed49 · outbound

This paper cites Control-oriented modeling of soft robotic swimmer with Koop- man operators,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Control-oriented modeling of soft robotic swimmer with Koop- man operators,

Reference 23

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation e598e302-7192-46da-b405-c4a4cb922d5e · outbound

This paper cites Global stability analysis using the eigen- functions of the Koopman operator,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Global stability analysis using the eigen- functions of the Koopman operator,

Reference 24

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 14815956-490f-42be-b338-f83b09e30362 · outbound

This paper cites Dynamic mode decomposition of numerical and experi- mental data,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Dynamic mode decomposition of numerical and experi- mental data,

Reference 25

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unresolved
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 5f8338fa-177d-4c74-ab8d-170c609d70ef · outbound

This paper cites Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses,

Reference 26

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation fffc8e15-c5de-4935-9f96-8fd466f3e6b9 · outbound

This paper cites On dynamic mode decomposition: theory and applications,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition On dynamic mode decomposition: theory and applications,

Reference 27

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 2f8415f3-02ff-401a-bb33-59101df1b52d · outbound

This paper cites Dynamic mode decomposition for large and streaming datasets,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Dynamic mode decomposition for large and streaming datasets,

Reference 28

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 97cf3f05-f8c4-4373-af03-b597c3241014 · outbound

This paper cites Online dynamic mode decomposition for time-varying systems,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Online dynamic mode decomposition for time-varying systems,

Reference 29

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 77923b4a-d0e3-4396-be4d-2058ef865e82 · outbound

This paper cites A parallel and streaming dynamic mode decomposition algorithm with finite precision error analysis for large data,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition A parallel and streaming dynamic mode decomposition algorithm with finite precision error analysis for large data,

Reference 30

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 84f5b8e5-32eb-4c22-a907-e9864a2f4b15 · outbound

This paper cites Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition,

Reference 31

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 6d180950-bd06-40e7-a72f-b1383aace70b · outbound

This paper cites De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets,

Reference 32

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation dd5b3b27-fef3-46da-9333-cf7da35744a1 · outbound

This paper cites Sparsity-promoting dynamic mode decomposition,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Sparsity-promoting dynamic mode decomposition,

Reference 33

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unresolved
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 70fc8f50-19b9-4583-ae55-26c20849914d · outbound

This paper cites Higher-order dynamic mode decom- position,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Higher-order dynamic mode decom- position,

Reference 34

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verified fuzzy
raw_fallback, observed 2026-08-14T05:28:31.647137Z

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Observation e0fecd8a-532e-43c8-957e-99a8356483fd · outbound

This paper cites A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,

Reference 35

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Observation fc7391e7-f37c-4ac5-ac1a-570f889aa370 · outbound

This paper cites On convergence of extended dynamic mode decomposition to the Koopman operator,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition On convergence of extended dynamic mode decomposition to the Koopman operator,

Reference 36

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Observation 5944c714-6dfe-4db7-a379-36bee2701b06 · outbound

This paper cites Approximating the Koopman operator using noisy data: noise-resilient extended dynamic mode decomposition,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Approximating the Koopman operator using noisy data: noise-resilient extended dynamic mode decomposition,

Reference 37

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Observation 09235291-7c11-4339-9a97-2dc001b0bb86 · outbound

This paper cites Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems,

Reference 38

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source=pdf_text observed=2026-08-14T05:28:29.927585Z digest=sha256:497f218bdd1d434ba026793e6720456c58e226ede4ddef10133164564a2046ec

Observation cc547396-c76b-4be5-b2da-5002a119af74 · outbound

This paper cites Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator,

Reference 39

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Observation 6aba9d3d-bb78-42bc-949c-e37a643152b0 · outbound

This paper cites Learning Koopman invariant subspaces for dynamic mode decomposition,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Learning Koopman invariant subspaces for dynamic mode decomposition,

Reference 40

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Observation b2dc3b78-fd09-432e-b964-e01e696d65c4 · outbound

This paper cites Learning deep neural network representations for Koopman operators of nonlinear dynamical systems,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Learning deep neural network representations for Koopman operators of nonlinear dynamical systems,

Reference 41

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source=pdf_text observed=2026-08-14T05:28:29.938638Z digest=sha256:223dfad90366feedad702077620fad0bd734d12702488103bd30df59e71741c4

Observation ad5e63eb-f4d9-4975-a7f5-20c288b623bc · outbound

This paper cites Linearly recurrent autoencoder networks for learning dynamics,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Linearly recurrent autoencoder networks for learning dynamics,

Reference 42

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Observation 6f3da56a-a4c8-405d-aabf-3f70d1cd2616 · outbound

This paper cites Koop- man invariant subspaces and finite linear representations of nonlinear dynamical systems for control,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Koop- man invariant subspaces and finite linear representations of nonlinear dynamical systems for control,

Reference 43

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Observation a2356d4f-c7be-47da-9eba-9c8d10833723 · outbound

This paper cites Optimal construction of Koopman eigen- functions for prediction and control,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Optimal construction of Koopman eigen- functions for prediction and control,

Reference 44

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Observation cb581edd-8f9c-476a-bef3-4b5da960fb94 · outbound

This paper cites Data-driven approximation of the Koopman generator: Model reduction, system identification, and control.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

Reference 45

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Observation e7f1b50e-2c95-4e1e-aede-d968dcb9b596 · outbound

This paper cites an unresolved cited work.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Unresolved cited work

Reference 46

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Observation 899bc263-1573-4476-a325-7865c15a2001 · outbound

This paper cites Optimal construction of Koopman eigenfunctions for prediction and control,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Optimal construction of Koopman eigenfunctions for prediction and control,

Reference 47

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Observation 25ba6638-5e58-4f72-8cb7-6ad740bc5c40 · outbound

This paper cites Tutorial: Complexity analysis of Singular Value Decomposition and its variants.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Tutorial: Complexity analysis of Singular Value Decomposition and its variants

Reference 48

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Observation b67a687f-a2c6-4c30-b2eb-f6048c14a34c · outbound

This paper cites Symmetric gauge functions and unitarily invariant norms,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Symmetric gauge functions and unitarily invariant norms,

Reference 49

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Observation 559c450c-d017-4286-8c81-026f43fbb296 · outbound

This paper cites Overview of total least-squares meth- ods,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Overview of total least-squares meth- ods,

Reference 50

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Observation b586d821-b832-4ee7-9577-115de7bb448d · outbound

This paper cites The approximation of one matrix by another of lower rank,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition The approximation of one matrix by another of lower rank,

Reference 51

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Observation bdfe2892-0b9e-4518-aebd-347108c82432 · outbound

This paper cites Non-local linearization of nonlinear differential equations via polyflows,.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition Non-local linearization of nonlinear differential equations via polyflows,

Reference 52

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Observation 8144b77d-f1c0-41af-8d1f-da05d5f64fc6 · outbound

This paper cites degree, in 2013, and M.Sc.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition degree, in 2013, and M.Sc

Reference 1991

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source=pdf_text observed=2026-08-14T05:28:30.181235Z digest=sha256:3ef18a1286de7bf8e4f649f74c85c4359f29ccf670805dba5a220b13ff1f50d2

Observation 4227d4f5-9a84-498f-a0bd-fba4f560a922 · outbound

This paper cites He was an Assistant Professor with the Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA, USA, from 2004 to 2007.

Learning Koopman Eigenfunctions and Invariant Subspaces from Data: Symmetric Subspace Decomposition He was an Assistant Professor with the Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA, USA, from 2004 to 2007

Reference 2001

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