Pith Number

pith:NKHJYX62

pith:2026:NKHJYX623R2W2F5D5XNC2LYIZP

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Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework

Cankat Tilki, Serkan Gugercin

Wavelet-based observables act as eigenfunctions of the Koopman semigroup, yielding closed-form expressions for its action and a new approximation algorithm.

arxiv:2605.14224 v1 · 2026-05-14 · math.NA · cs.AI · cs.NA · math.DS · math.FA

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Claims

C1strongest claim

Wavelet-based observables are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm; closed-form expressions for the semigroup and resolvent follow, and the cWDMD algorithm approximates the action numerically.

C2weakest assumption

That the wavelet-based observables remain eigenfunctions and yield useful approximations for the specific dynamical systems and function spaces encountered in applications, beyond the two numerical examples shown.

C3one line summary

Wavelet-based observables are eigenfunctions of the Koopman semigroup, yielding closed-form expressions and the cWDMD algorithm that extends EDMD for numerical approximation, validated on two examples.

References

55 extracted · 55 resolved · 0 Pith anchors

[1] A. C. Antoulas, C. A. Beattie, and S. G¨ u˘ gercin. Interpolatory Methods for Model Reduction. Society for Industrial and Applied Mathematics, Philadel phia, PA, 2020 2020

[2] P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W . Schilders, and L. M. Sil- veira, editors. Model Order Reduction: Volume 1: System- and Data-Driven Me thods and Algorithms . De Gruyter, Berl 2021

[3] M. Berljafa and S. G¨ uttel. The RKFIT algorithm for nonli near rational approxima- tion. SIAM Journal on Scientiﬁc Computing , 39(5):A2049–A2071, 2017. Preprint. 2026-05-15 C.Tilki, S.G¨ u˘ gercin: W 2017

[4] S. L. Brunton, M. Budiˇ si´ c, E. Kaiser, and J. N. Kutz. Mod ern Koopman theory for dynamical systems. SIAM Review , 64(2):229–340, 2022 2022

[5] A. Coddington and N. Levinson. Theory of Ordinary Diﬀerential Equations . Inter- national series in pure and applied mathematics. McGraw-Hi ll, 1955 1955

Receipt and verification

First computed	2026-05-17T23:39:10.796216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a8e9c5fdadc756d17a3edda2d2f08cbdcb89ab608f1da87c7dfe4e6e46d1b41

Aliases

arxiv: 2605.14224 · arxiv_version: 2605.14224v1 · doi: 10.48550/arxiv.2605.14224 · pith_short_12: NKHJYX623R2W · pith_short_16: NKHJYX623R2W2F5D · pith_short_8: NKHJYX62

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/NKHJYX623R2W2F5D5XNC2LYIZP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6a8e9c5fdadc756d17a3edda2d2f08cbdcb89ab608f1da87c7dfe4e6e46d1b41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf3f5145b8bb63246210fb06856288df0657358b35ad87f979ae1562869811b8",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.NA",
      "math.DS",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-14T00:35:05Z",
    "title_canon_sha256": "028abdd6b1e5186b8480c6e20a7a06a4d8da1e261bf2ea548bdf6bf79a9d6075"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14224",
    "kind": "arxiv",
    "version": 1
  }
}