Paper Citation Record · LEDGER

The Logarithmic Laplacian on General Graphs

As of 20 August 2026, this Paper Citation Record lists 73 of 73 outbound references and 2 inbound Pith citation observations for arXiv:2507.05936.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.05936 v2

Coverage vector

measured 73 of 73 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:32:12.915838Z

measured 75 of 75 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T12:43:29.044156Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-04T06:49:38.094077Z

Reference resolution

73 of 73 outbound references displayed

verified exact7
verified fuzzy58
unresolved8
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 98b70592-d4d7-4b9c-af10-c4e99e465a0a · outbound

This paper cites An extension problem related to the fractional laplacian.

The Logarithmic Laplacian on General Graphs An extension problem related to the fractional laplacian

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.739063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 799fcc8a-2595-44b3-adf3-0853351d2547 · outbound

This paper cites Hitchhiker’s guide to the fractional sobolev spaces.Bulletin des sciences math´ematiques, 136(5):521–573, 2012.

The Logarithmic Laplacian on General Graphs Hitchhiker’s guide to the fractional sobolev spaces.Bulletin des sciences math´ematiques, 136(5):521–573, 2012

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.728309Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a12855cd-7877-43e9-85b7-f3f0504afdc9 · outbound

This paper cites Ten equivalent definitions of the fractional laplace operator.

The Logarithmic Laplacian on General Graphs Ten equivalent definitions of the fractional laplace operator

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.717904Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1814e3b1-cb64-44e1-8875-1ff28d5b8964 · outbound

This paper cites Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation.

The Logarithmic Laplacian on General Graphs Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.707358Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 50c3c9b4-ca0a-47ec-9a4b-acf19672bc10 · outbound

This paper cites The dirichlet problem for the fractional lapla- cian: regularity up to the boundary.

The Logarithmic Laplacian on General Graphs The dirichlet problem for the fractional lapla- cian: regularity up to the boundary

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.696652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f6903c92-0738-47b4-bc43-1d59ddcac8f1 · outbound

This paper cites Extension problem and harnack’s inequality for some fractional operators.

The Logarithmic Laplacian on General Graphs Extension problem and harnack’s inequality for some fractional operators

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.686826Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 523ff279-3a6d-4067-8a2c-33a3b31d5644 · outbound

This paper cites Mountain pass solutions for non-local elliptic operators.

The Logarithmic Laplacian on General Graphs Mountain pass solutions for non-local elliptic operators

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.674905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3c7fce0d-b8ac-4ac0-9ebb-26bba4f2b9ad · outbound

This paper cites Variational methods for non-local oper- ators of elliptic type.

The Logarithmic Laplacian on General Graphs Variational methods for non-local oper- ators of elliptic type

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.663646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a1dbe06d-2af1-4d07-bb8c-946266f6acc2 · outbound

This paper cites Eigenvalues of the fractional laplace operator in the interval.

The Logarithmic Laplacian on General Graphs Eigenvalues of the fractional laplace operator in the interval

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.652756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a8a3cf8a-9583-414f-b947-17b00217e371 · outbound

This paper cites Small order asymptotics of the dirichlet eigenvalue problem for the fractional laplacian.

The Logarithmic Laplacian on General Graphs Small order asymptotics of the dirichlet eigenvalue problem for the fractional laplacian

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.642039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a68e7975-b06d-4aeb-aa66-cce3b0c9d487 · outbound

This paper cites The dirichlet problem for the logarithmic laplacian.

The Logarithmic Laplacian on General Graphs The dirichlet problem for the logarithmic laplacian

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.631231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0222f533-495f-44ca-ae62-2fffb65bf266 · outbound

This paper cites Bounds for eigenvalues of the dirichlet problem for the logarithmic laplacian.

The Logarithmic Laplacian on General Graphs Bounds for eigenvalues of the dirichlet problem for the logarithmic laplacian

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.621111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation aa38c320-840b-4fe8-a381-5d39042c39e6 · outbound

This paper cites Spectral properties of the logarithmic laplacian.Analysis and Mathematical Physics, 11:1–24, 2021.

The Logarithmic Laplacian on General Graphs Spectral properties of the logarithmic laplacian.Analysis and Mathematical Physics, 11:1–24, 2021

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.610613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b3564330-477b-4b35-8746-15ec217503ef · outbound

This paper cites The cauchy problem associated to the logarithmic laplacian with an application to the fundamental solution.

The Logarithmic Laplacian on General Graphs The cauchy problem associated to the logarithmic laplacian with an application to the fundamental solution

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.600001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation bee024c9-828d-4a30-9321-698d8715a553 · outbound

This paper cites A new look at the fractional poisson problem via the logarithmic laplacian.

The Logarithmic Laplacian on General Graphs A new look at the fractional poisson problem via the logarithmic laplacian

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.589271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 47938c02-f4f5-4b4e-a825-774383534fba · outbound

This paper cites An extension problem for the logarithmic Laplacian.

The Logarithmic Laplacian on General Graphs An extension problem for the logarithmic Laplacian

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.699558Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef173f8f-b262-4801-b738-e70d8ffdd500 · outbound

This paper cites A direct method of moving planes for the logarith- mic laplacian.

The Logarithmic Laplacian on General Graphs A direct method of moving planes for the logarith- mic laplacian

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.578746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 12ba8df4-d955-45ee-8061-e02c3f6c29ee · outbound

This paper cites Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian.

The Logarithmic Laplacian on General Graphs Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:13.105051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a3676bc0-b79e-4e25-bb5d-cc64b95bd215 · outbound

This paper cites The $0$-fractional perimeter between fractional perimeters and Riesz potentials.

The Logarithmic Laplacian on General Graphs The $0$-fractional perimeter between fractional perimeters and Riesz potentials

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:13.090293Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9b1cd073-1f8e-4e3b-8d84-95708537ac2c · outbound

This paper cites Fractional cauchy problems on compact manifolds.

The Logarithmic Laplacian on General Graphs Fractional cauchy problems on compact manifolds

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.568855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4ebaef85-2587-4292-ade3-a61e6e02f52a · outbound

This paper cites Fractional calder ´on problem on a closed riemannian manifold.

The Logarithmic Laplacian on General Graphs Fractional calder ´on problem on a closed riemannian manifold

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.557722Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8d3922df-3944-4442-8d99-2bc21ffb522e · outbound

This paper cites An inverse problem for the space-time fractional Schr\"odinger equation on closed manifolds.

The Logarithmic Laplacian on General Graphs An inverse problem for the space-time fractional Schr\"odinger equation on closed manifolds

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:13.076192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4cd8949b-5bed-4c2e-bb93-2d3416f41f95 · outbound

This paper cites Fractional Laplacians on the sphere, the Minakshisundaram zeta function and semigroups.

The Logarithmic Laplacian on General Graphs Fractional Laplacians on the sphere, the Minakshisundaram zeta function and semigroups

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:13.060741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d0615d6a-2f2b-4faf-a3d1-04dd6ac867af · outbound

This paper cites Some constructions for the fractional laplacian on noncompact manifolds.

The Logarithmic Laplacian on General Graphs Some constructions for the fractional laplacian on noncompact manifolds

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.547316Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 58907068-447a-4453-ba81-74c54b36356e · outbound

This paper cites Asymptotics as $s \to 0^+$ of the fractional perimeter on Riemannian manifolds.

The Logarithmic Laplacian on General Graphs Asymptotics as $s \to 0^+$ of the fractional perimeter on Riemannian manifolds

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.736458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation feee5463-c474-4140-b496-5df4fa121524 · outbound

This paper cites Fractional sobolev spaces on riemannian manifolds.

The Logarithmic Laplacian on General Graphs Fractional sobolev spaces on riemannian manifolds

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.536687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2c4467ea-bb35-40cb-92ec-df2fcb0cf853 · outbound

This paper cites An extension problem and hardy’s inequal- ity for the fractional laplace-beltrami operator on riemannian symmetric spaces of noncompact type.

The Logarithmic Laplacian on General Graphs An extension problem and hardy’s inequal- ity for the fractional laplace-beltrami operator on riemannian symmetric spaces of noncompact type

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.526841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1bcd82eb-8daa-40b1-a960-0f1846c7600f · outbound

This paper cites Asymptotic behavior of solutions to the extension problem for the fractional laplacian on noncompact symmetric spaces.

The Logarithmic Laplacian on General Graphs Asymptotic behavior of solutions to the extension problem for the fractional laplacian on noncompact symmetric spaces

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.516584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3e993da0-1091-4de2-9671-c219182d4fd4 · outbound

This paper cites Integral representa- tion for fractional laplace–beltrami operators.

The Logarithmic Laplacian on General Graphs Integral representa- tion for fractional laplace–beltrami operators

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.505380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 22a71c40-0c38-4552-8ed9-3ac1eacaedae · outbound

This paper cites Large-time behavior of two families of operators related to the fractional laplacian on certain riemannian manifolds.

The Logarithmic Laplacian on General Graphs Large-time behavior of two families of operators related to the fractional laplacian on certain riemannian manifolds

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.494204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1073ed69-c7a3-4817-a8d0-665d237a6778 · outbound

This paper cites Harnack inequality for nonlocal operators on manifolds with nonnegative curvature.

The Logarithmic Laplacian on General Graphs Harnack inequality for nonlocal operators on manifolds with nonnegative curvature

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.483896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3d882241-7104-4997-a10a-2b8fe399b0d7 · outbound

This paper cites The Schr\"odinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees.

The Logarithmic Laplacian on General Graphs The Schr\"odinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:13.036313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 789ca89f-67e2-4958-afb5-18807a5ccd59 · outbound

This paper cites Anisotropic Calder\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$.

The Logarithmic Laplacian on General Graphs Anisotropic Calder\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:13.020739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f0b646d6-3ee8-40b6-84cc-06d3c6e1bbfe · outbound

This paper cites Logarithmic Laplacian on General Riemannian Manifolds.

The Logarithmic Laplacian on General Graphs Logarithmic Laplacian on General Riemannian Manifolds

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.770256Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e15a30d5-46e4-4fc2-9241-06f6d9c07d60 · outbound

This paper cites Spectral graph theory, volume 92.

The Logarithmic Laplacian on General Graphs Spectral graph theory, volume 92

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.473560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3ca51cf7-1a73-4e22-8d38-cf81af604016 · outbound

This paper cites Coverings, heat kernels and spanning trees.

The Logarithmic Laplacian on General Graphs Coverings, heat kernels and spanning trees

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.463423Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 18c5c002-4a05-4791-b36b-dbfe309462d9 · outbound

This paper cites Sharp davies–gaffney–grigor’yan lemma on graphs.

The Logarithmic Laplacian on General Graphs Sharp davies–gaffney–grigor’yan lemma on graphs

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.453421Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8e3a4772-0e54-42f9-8ceb-5a10dad5aede · outbound

This paper cites Heat kernel and essential spectrum of infinite graphs.

The Logarithmic Laplacian on General Graphs Heat kernel and essential spectrum of infinite graphs

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.443309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4e5be4f4-3838-456e-8e54-132b36ce2df1 · outbound

This paper cites Stochastic completeness of graphs.

The Logarithmic Laplacian on General Graphs Stochastic completeness of graphs

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.433560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e181dbf3-bf48-4c89-b360-8ceb71ab8b91 · outbound

This paper cites an unresolved cited work.

The Logarithmic Laplacian on General Graphs Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:32:13.423816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 84d12d05-8aa1-4b23-b471-7e6331473ec6 · outbound

This paper cites Li-yau inequality on graphs.

The Logarithmic Laplacian on General Graphs Li-yau inequality on graphs

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.414132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 04087e00-0128-4533-a72d-42f314e2ca7c · outbound

This paper cites Existence of ground state solutions to some nonlinear schr¨odinger equations on lattice graphs.

The Logarithmic Laplacian on General Graphs Existence of ground state solutions to some nonlinear schr¨odinger equations on lattice graphs

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.403196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8c5dfc28-6e1e-482d-b84f-3f360cc6486c · outbound

This paper cites Normalized solutions for nonlinear schr¨odinger equa- tions on graphs.

The Logarithmic Laplacian on General Graphs Normalized solutions for nonlinear schr¨odinger equa- tions on graphs

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.392708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fe080419-8288-43ad-9913-e9944ffc3b30 · outbound

This paper cites Existence of positive solutions to some nonlinear equations on locally finite graphs.

The Logarithmic Laplacian on General Graphs Existence of positive solutions to some nonlinear equations on locally finite graphs

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.382185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 80c7257e-0e38-4f5f-9b46-c30292cb88b4 · outbound

This paper cites Convergence of ground state solutions for nonlinear schr¨odinger equations on graphs.

The Logarithmic Laplacian on General Graphs Convergence of ground state solutions for nonlinear schr¨odinger equations on graphs

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.371206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 41d77ef6-f78a-4dfc-a111-b61be2c8422f · outbound

This paper cites Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs.

The Logarithmic Laplacian on General Graphs Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.814254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 517e8482-902a-4f10-af75-7c24eb1aa220 · outbound

This paper cites Fractional Laplace operator on finite graphs.

The Logarithmic Laplacian on General Graphs Fractional Laplace operator on finite graphs

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.817991Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cac2aa0f-cb6d-4600-a4fd-3df6f221ebd1 · outbound

This paper cites Nonlocal discrete diffusion equations and the fractional discrete laplacian, regularity and applications.

The Logarithmic Laplacian on General Graphs Nonlocal discrete diffusion equations and the fractional discrete laplacian, regularity and applications

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.361168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c732ad8a-088e-43db-b1b4-a192c644d92a · outbound

This paper cites Convergence of least energy sign-changing solutions for logarithmic schr¨odinger equations on locally finite graphs.

The Logarithmic Laplacian on General Graphs Convergence of least energy sign-changing solutions for logarithmic schr¨odinger equations on locally finite graphs

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.351272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9e069bef-8a1a-40ab-a9ad-05a35c5970d8 · outbound

This paper cites Existence and multiplicity of solutions for the logarithmic schr¨odinger equation with a potential on lattice graphs.

The Logarithmic Laplacian on General Graphs Existence and multiplicity of solutions for the logarithmic schr¨odinger equation with a potential on lattice graphs

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.340935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7ff923c3-15bd-45bc-bc1d-e79a886a52b4 · outbound

This paper cites Existence and stability of standing waves for nonlinear fractional schr¨odinger equation with logarithmic nonlinearity.

The Logarithmic Laplacian on General Graphs Existence and stability of standing waves for nonlinear fractional schr¨odinger equation with logarithmic nonlinearity

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.330229Z

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Observation 9c6f7453-ac36-4646-87b1-9590361f650a · outbound

This paper cites Ground states for logarithmic schr¨odinger equations on locally finite graphs.

The Logarithmic Laplacian on General Graphs Ground states for logarithmic schr¨odinger equations on locally finite graphs

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.318634Z

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Observation 32ca765e-7145-4a0b-9ce0-106c0bc5164b · outbound

This paper cites Eigenvalue estimates for the fractional Laplacian on lattice subgraphs.

The Logarithmic Laplacian on General Graphs Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.842107Z

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Observation 19171168-7e1d-4581-b826-dd459927ceaf · outbound

This paper cites Some theorems on stable processes.

The Logarithmic Laplacian on General Graphs Some theorems on stable processes

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.308400Z

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Observation ed4675d6-ac55-40f9-9408-d9f854407a6f · outbound

This paper cites Classical fourier analysis, volume 2.

The Logarithmic Laplacian on General Graphs Classical fourier analysis, volume 2

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.296931Z

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Observation 4cb52678-7385-4d6a-a4c2-539332c6a7f2 · outbound

This paper cites Alpha-stable random walk has massive thorns.

The Logarithmic Laplacian on General Graphs Alpha-stable random walk has massive thorns

Reference 56

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:32:12.964955Z

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Observation 1015add5-7f15-4d79-9952-ec7d76a6c1b1 · outbound

This paper cites Stochastic completeness for graphs with curvature dimen- sion conditions.

The Logarithmic Laplacian on General Graphs Stochastic completeness for graphs with curvature dimen- sion conditions

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.286001Z

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Observation d911a0a1-63af-4b3e-acb1-eeef53a0cf1a · outbound

This paper cites Volume growth and stochastic completeness of graphs.

The Logarithmic Laplacian on General Graphs Volume growth and stochastic completeness of graphs

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.275580Z

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Observation a5d91e6d-e0fc-4028-bb9e-a37073c41388 · outbound

This paper cites Springer, 2021.

The Logarithmic Laplacian on General Graphs Springer, 2021

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.266194Z

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Observation 3c797fd4-7d76-4489-9ada-df1a24e1bb4e · outbound

This paper cites Dirichlet forms and stochastic completeness of graphs and subgraphs.

The Logarithmic Laplacian on General Graphs Dirichlet forms and stochastic completeness of graphs and subgraphs

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.256635Z

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Observation 2f869218-7b53-4b66-b277-53714898fbee · outbound

This paper cites Fractional logarithmic Schr\"{o}dinger equations on lattice graphs.

The Logarithmic Laplacian on General Graphs Fractional logarithmic Schr\"{o}dinger equations on lattice graphs

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-06T19:32:12.872015Z

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Observation bfd069e4-437b-4141-b3c0-f277c42c3d61 · outbound

This paper cites Heat kernels and spectral theory.

The Logarithmic Laplacian on General Graphs Heat kernels and spectral theory

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.246564Z

Source-reported events for the cited work

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Observation 6cf40120-84c8-403f-b94b-e5b851df1636 · outbound

This paper cites Heat kernel and analysis on manifolds, volume 47.

The Logarithmic Laplacian on General Graphs Heat kernel and analysis on manifolds, volume 47

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.236359Z

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Observation 343fb334-9b79-484c-8389-dc850e5e2ad2 · outbound

This paper cites On the parabolic kernel of the schr ¨odinger operator.

The Logarithmic Laplacian on General Graphs On the parabolic kernel of the schr ¨odinger operator

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.225942Z

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Observation 5d24b759-c89c-43a3-8cc4-505d2cb05eed · outbound

This paper cites Grigoryan T.

The Logarithmic Laplacian on General Graphs Grigoryan T

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.215208Z

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Observation 0931a56d-47ae-455a-87b1-0d1af53917cd · outbound

This paper cites Global gradient estimate on graph and its applications.

The Logarithmic Laplacian on General Graphs Global gradient estimate on graph and its applications

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.204616Z

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Observation 47fe065b-01d2-473c-a71d-cd6b3e07095f · outbound

This paper cites A gradient estimate for positive functions on graphs.

The Logarithmic Laplacian on General Graphs A gradient estimate for positive functions on graphs

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.194285Z

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Observation 403f1ff0-b95c-4ee5-be33-967b556400d1 · outbound

This paper cites Large deviations for heat kernels on graphs.

The Logarithmic Laplacian on General Graphs Large deviations for heat kernels on graphs

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.183057Z

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Observation 8cb10acd-34a0-487f-8171-61e1796e3c33 · outbound

This paper cites Gaussian upper bounds for heat kernels of continuous time simple random walks.

The Logarithmic Laplacian on General Graphs Gaussian upper bounds for heat kernels of continuous time simple random walks

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.169954Z

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Observation 8cbc92b4-3f6f-4ecc-9a37-d9d51154a1e1 · outbound

This paper cites Parabolic harnack inequality and estimates of markov chains on graphs.

The Logarithmic Laplacian on General Graphs Parabolic harnack inequality and estimates of markov chains on graphs

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.159409Z

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Observation 3abd73fe-15e8-402d-8ffb-4573b1c7ff6e · outbound

This paper cites On-diagonal lower estimate of heat kernels on graphs.

The Logarithmic Laplacian on General Graphs On-diagonal lower estimate of heat kernels on graphs

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.147641Z

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Observation fa4ecf26-e246-4af8-9120-0a60551ce57c · outbound

This paper cites NIST handbook of mathematical functions hardback and CD-ROM.

The Logarithmic Laplacian on General Graphs NIST handbook of mathematical functions hardback and CD-ROM

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.136018Z

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Observation 8ea6ff8c-7e12-4ba7-aa60-f966d40b6af6 · outbound

This paper cites Singular integrals and differentiability properties of functions.

The Logarithmic Laplacian on General Graphs Singular integrals and differentiability properties of functions

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:32:13.125298Z

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Pith citing papers

Observation c2082c18-b6a2-4c00-b9ca-9f9504c6757a · inbound

Extension theorems for logarithmic Schr\"odinger and discrete Laplacian operators cites this paper.

Extension theorems for logarithmic Schr\"odinger and discrete Laplacian operators The Logarithmic Laplacian on General Graphs

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-13T12:43:29.044156Z

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Observation e37120aa-d90f-4d27-becd-07c5fcd6bc3e · inbound

On $m$-order logarithmic Schr\"odinger operator cites this paper.

On $m$-order logarithmic Schr\"odinger operator The Logarithmic Laplacian on General Graphs

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-04T06:49:38.095882Z

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