Pith Number

pith:W3ACHFOX

pith:2026:W3ACHFOXLD5VJMFCCU3BJDWJ3X

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Nonuniform Periodic Wavelet Frames on Non-Archimedean Fields

Owais Ahmad

Nonuniform periodic wavelet frames on non-Archimedean fields are constructed using Fourier transforms and the unitary extension principle.

arxiv:2605.17323 v1 · 2026-05-17 · math.FA · math-ph · math.MP

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Claims

C1strongest claim

we introduce a notion of nonuniform periodic wavelet frame on non-Archimedean field. Using Fourier transform technique and the unitary extension principle, we propose an approach for the construction of nonuniform periodic wavelet frames on non-Archimedean fields.

C2weakest assumption

The spectral-pair and nonuniform multiresolution analysis ideas developed for the real line extend to non-Archimedean fields in a way that preserves the necessary unitary and frame properties.

C3one line summary

The authors construct nonuniform periodic wavelet frames on non-Archimedean fields via Fourier transform techniques and the unitary extension principle.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] O. Ahmad and N. A. Sheikh, On Characterization of nonuniform tight wavelet frames on local fields,Anal. Theory Appl.,34(2018) 135-146 2018

[2] J.J. Benedetto and R.L. Benedetto, A wavelet theory for local fields and related groups. J. Geom. Anal.14(2004) 423-456 2004

[3] Christensen,An Introduction to Frames and Riesz Bases, Second Edition, Birkh¨ auser, Boston, 2016 2016

[4] I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-based constructions of wavelet frames,Appl. Comput. Harmon. Anal.14(2003) 1-46 2003

[5] I. Daubechies, A. Grossmann, Y. Meyer, Painless non-orthogonal expansions,J. Math. Phys.27(5) (1986) 1271-1283 1986

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:52.099944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6c02395d758fb54b0a21536148ec9ddcc2c81275be4fc4b89b23f5dab1afa7f

Aliases

arxiv: 2605.17323 · arxiv_version: 2605.17323v1 · doi: 10.48550/arxiv.2605.17323 · pith_short_12: W3ACHFOXLD5V · pith_short_16: W3ACHFOXLD5VJMFC · pith_short_8: W3ACHFOX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W3ACHFOXLD5VJMFCCU3BJDWJ3X \
  | 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: b6c02395d758fb54b0a21536148ec9ddcc2c81275be4fc4b89b23f5dab1afa7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afa0a48eb35dc607061ac13b5e975ea5dda4bfeebb1f16d64d4aaff847f98fb5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-17T08:29:51Z",
    "title_canon_sha256": "9f23059bbfb31e703de5714bd60599cf9c6ad848d62291bdb8b236261e6ba71f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17323",
    "kind": "arxiv",
    "version": 1
  }
}