Pith Number

pith:RNCOYXTQ

pith:2025:RNCOYXTQJWSVRSVW6UJ4GJYPL3

not attested not anchored not stored refs pending

Sampling on Paley-Wiener spaces on graphs, with particular focus on the infinite-dimensional case

Filippo Giannoni

Sampling sets for Paley-Wiener spaces on graphs are exactly the complements of lambda-sets.

arxiv:2511.17343 v6 · 2025-11-21 · math.FA

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Claims

C1strongest claim

We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where a Poincaré-type inequality holds), thereby providing a sufficient condition for stable sampling and reconstruction on graphs such as Z^n-lattices and radial trees with finite geometry.

C2weakest assumption

The graphs admit a well-defined infinite-dimensional Paley-Wiener space in which the Poincaré-type inequality on lambda-sets is both necessary and sufficient for the sampling theorem to hold.

C3one line summary

Sampling sets for infinite-dimensional Paley-Wiener spaces on graphs are exactly the complements of lambda-sets where a Poincaré inequality holds, enabling stable reconstruction.

Receipt and verification

First computed	2026-05-29T02:05:38.002368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b44ec5e704da558cab6f513c3270f5ed310d90b46d6bdf7d34e18b8716f9429

Aliases

arxiv: 2511.17343 · arxiv_version: 2511.17343v6 · doi: 10.48550/arxiv.2511.17343 · pith_short_12: RNCOYXTQJWSV · pith_short_16: RNCOYXTQJWSVRSVW · pith_short_8: RNCOYXTQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RNCOYXTQJWSVRSVW6UJ4GJYPL3 \
  | 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: 8b44ec5e704da558cab6f513c3270f5ed310d90b46d6bdf7d34e18b8716f9429

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07234b4e5705030424274652db55a5054daf7902d06419436a7181392f828297",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-11-21T16:04:53Z",
    "title_canon_sha256": "4d10dd9988cd3814ceae925703f49a21d4e8f9f684fe0ddf975d6c64e3f7bbce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.17343",
    "kind": "arxiv",
    "version": 6
  }
}