Pith Number

pith:4GQ4UCP3

pith:2026:4GQ4UCP3USLDH7XTYGHIWQV3QV

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Eigenvalue bounds for non-self-adjoint Schr\"odinger operators and pseudodifferential generalizations

Eduard Stefanescu

Eigenvalue bounds for non-self-adjoint Schrödinger operators extend to fractional Laplacians on compact manifolds via L^p norms of the potentials.

arxiv:2605.16569 v1 · 2026-05-15 · math.SP · math-ph · math.MP

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Record completeness

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Claims

C1strongest claim

We extend the result on spectral bounds on compact manifolds to the case of fractional Laplacians, applying methods by Cuenin and Sogge. These bounds are formulated in terms of the L^p-norms of the corresponding potentials.

C2weakest assumption

The adaptation of Cuenin-Sogge methods to the fractional Laplacian on compact manifolds works without extra restrictions on the potential or the geometry beyond those already present in the cited works.

C3one line summary

Survey of eigenvalue bounds for non-self-adjoint Schrödinger operators with complex potentials, plus a new extension to fractional Laplacians on manifolds via L^p-norm estimates.

References

64 extracted · 64 resolved · 0 Pith anchors

[1] A. A. Abramov, A. A. Aslanyan, and E. B. Davies. Bounds on complex eigenvalues and resonances.Journal of Physics A, 34:57–72, 1999 1999

[2] J. Aguilar and J.-M. Combes. A class of analytic perturbations for one-body Schrödinger hamiltonians. Communications in Mathematical Physics, 22(4):269–279, Dec. 1971 1971

[3] E. Balslev and J.-M. Combes. Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions.Communications in Mathematical Physics, 22(4):280–294, Dec. 1971 1971

[4] M. S. Birman. On the spectrum of singular boundary-value problems.Matematicheskii Sbornik. New Series, 55(2):125–174, 1961 1961

[5] M. S. Birman. Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions.Vestnik Leningradskogo Universiteta, 1(1):22–55, 1962. (in Ru 1962

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:02:29.652989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1a1ca09fba49633fef3c18e8b42bb8578dd854464a3d50d07c3c5dce599953b

Aliases

arxiv: 2605.16569 · arxiv_version: 2605.16569v1 · doi: 10.48550/arxiv.2605.16569 · pith_short_12: 4GQ4UCP3USLD · pith_short_16: 4GQ4UCP3USLDH7XT · pith_short_8: 4GQ4UCP3

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4GQ4UCP3USLDH7XTYGHIWQV3QV \
  | 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: e1a1ca09fba49633fef3c18e8b42bb8578dd854464a3d50d07c3c5dce599953b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8acca9acc16e64ef9aaaf74fa10deb120efb263057c84c75474b056bcc2b8ebc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-05-15T19:16:22Z",
    "title_canon_sha256": "36e079deb151ed8bbb2f600a0c068862ff7de90b415012c0c42f87b11c7db220"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16569",
    "kind": "arxiv",
    "version": 1
  }
}