Pith Number

pith:Q2CHPNL3

pith:2026:Q2CHPNL3JOUIL3FVS2L4YROL3J

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Approximations with Non-Symmetric Green's Kernels and their Application to Fractional Differential Equations

Nick Fisher

Non-symmetric Green's kernels produce optimal-order spline interpolants for fractional differential equations in reproducing kernel Banach spaces.

arxiv:2605.12707 v1 · 2026-05-12 · math.NA · cs.NA

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Claims

C1strongest claim

we are able to prove that the proposed kernel interpolants obtain optimal order convergence rates in a reproducing kernel Banach space.

C2weakest assumption

The fractional differential operator admits a well-defined non-symmetric Green's kernel that can be used to construct the spline interpolant outside the reproducing kernel Hilbert space setting.

C3one line summary

Non-symmetric Green's kernels yield optimal-order convergent approximations for fractional differential equations in reproducing kernel Banach spaces.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] An introduction to the Hilbert-Schmidt SVD using iterated Brownian bridge kernels , author=. Numer. Algor. , volume=

[2] Variational formulation for the stationary fractional advection dispersion equation , author=. Num. Meth. for PDE's , volume=

[3] M. Esmaeilbeigi and O. Chatrabgoun and M. Cheraghi , journal=. The role of

[4] Total Positivity , author=

[5] Numerical simulation for solute transport in fractal porous media , author=. ANZIAM J. , volume=

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:49.600767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

868477b57b4ba885ecb59697cc45cbda51960f4913d62c76a996e9d0c47d0c84

Aliases

arxiv: 2605.12707 · arxiv_version: 2605.12707v1 · doi: 10.48550/arxiv.2605.12707 · pith_short_12: Q2CHPNL3JOUI · pith_short_16: Q2CHPNL3JOUIL3FV · pith_short_8: Q2CHPNL3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q2CHPNL3JOUIL3FVS2L4YROL3J \
  | 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: 868477b57b4ba885ecb59697cc45cbda51960f4913d62c76a996e9d0c47d0c84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2a999399e06034955ed7d3d41a15b0b7e265c6e163ec5d225056c62b9fe6ac6",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-12T20:09:42Z",
    "title_canon_sha256": "e5d43742cf40494a1e52f31b823f9f059dc1b55c28d0e55c0556840a0a5233b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12707",
    "kind": "arxiv",
    "version": 1
  }
}