Pith Number

pith:2YKTFTHO

pith:2025:2YKTFTHOXTIH5WYGD7AXHTHKQI

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On the existence of optimizers for nonlinear time-frequency concentration problems: the Wigner distribution

Erling A. T. Svela, Federico Stra, S. Ivan Trapasso

The nonlinear Wigner concentration problem admits an optimizer for any finite-measure phase space set and every p less than infinity.

arxiv:2510.18683 v3 · 2025-10-21 · math.CA · math.FA

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Record completeness

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Claims

C1strongest claim

For any measurable Ω ⊂ ℝ^{2d} with 0 < |Ω| < ∞ and any 1 ≤ p < ∞, the nonlinear concentration problem sup (||Wf||_{L^p(Ω)} / ||f||_{L^2}^2) admits an optimizer.

C2weakest assumption

The new asymptotic formula that quantifies the limiting contribution to concentration over Ω from asymptotically separated wave packets holds and can be combined with concentration compactness for Heisenberg-type dislocations to restore the necessary upper semicontinuity (abstract, section on main proof strategy).

C3one line summary

Existence of optimizers is established for the Wigner-distribution concentration functional over finite-measure phase-space sets for 1 ≤ p < ∞, with sharp constant 2^d attained at p = ∞.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] P. Boggiatto, G. De Donno, and A. Oliaro. Time-frequency representations of Wigner type and pseudo-differential operators.Trans. Amer. Math. Soc., 362(9), 2010 2010

[2] A. J. Bracken, H.-D. Doebner, and J. G. Wood. Bounds on integrals of the wigner function.Phys. Rev. Lett., 83, 1999 1999

[3] Cohen.Time-frequency analysis 1995

[4] L. Cohen. Uncertainty principles of the short-time fourier transform. InAdvanced Signal Processing Algorithms, volume 2563, pages 80–90. SPIE, 1995 1995

[5] E. Cordero, M. de Gosson, and F. Nicola. On the reduction of the interferences in the Born-Jordan distribution.Appl. Comput. Harmon. Anal., 44(2), 2018 2018

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-26T02:05:03.477560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d61532cceebcd07edb061fc173ccea822e3475a95ba2b7fb3db88d4c830c72c2

Aliases

arxiv: 2510.18683 · arxiv_version: 2510.18683v3 · doi: 10.48550/arxiv.2510.18683 · pith_short_12: 2YKTFTHOXTIH · pith_short_16: 2YKTFTHOXTIH5WYG · pith_short_8: 2YKTFTHO

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2YKTFTHOXTIH5WYGD7AXHTHKQI \
  | 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: d61532cceebcd07edb061fc173ccea822e3475a95ba2b7fb3db88d4c830c72c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97cc210e585e1883991fcb1f7f6e1c2b2fcfff2cb72be4acab399ca0a6ea0d41",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-10-21T14:40:34Z",
    "title_canon_sha256": "50cbf89cd6c46fbe84be09b1e8223fb8d4a3211d76a4e3cfbdeed873cc1417f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.18683",
    "kind": "arxiv",
    "version": 3
  }
}