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Paper Citation Record · LEDGER

An optimal fractional Hardy inequality on the discrete half-line

As of 8 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2507.06716.

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

pith.paper-citation-record.v1
2507.06716 v2

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:13:36.029823Z

measured 54 of 54 standing notices

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

54 of 54 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e3d048a8-59ce-4298-9430-b5f74c862d60 · outbound

This paper cites Stegun.Handbook of mathematical functions with formulas, graphs, and mathematical tables.

An optimal fractional Hardy inequality on the discrete half-line Stegun.Handbook of mathematical functions with formulas, graphs, and mathematical tables

Reference 1

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Observation 6f4eb0d9-af54-4eaf-9439-bc0119e17e66 · outbound

This paper cites FractionalboundaryHardyinequalityforthecritical cases, arXiv:2308.11956, 2024.

An optimal fractional Hardy inequality on the discrete half-line FractionalboundaryHardyinequalityforthecritical cases, arXiv:2308.11956, 2024

Reference 2

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This paper cites Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions ofN-body Schrödinger operators, volume 29 ofMathematical Notes.

An optimal fractional Hardy inequality on the discrete half-line Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions ofN-body Schrödinger operators, volume 29 ofMathematical Notes

Reference 3

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Observation dc480e54-b38f-4bb8-82eb-ee78e4f95999 · outbound

This paper cites Askey and Ranjan Roy.

An optimal fractional Hardy inequality on the discrete half-line Askey and Ranjan Roy

Reference 4

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Observation 486e743a-cdb8-43e1-8fd1-4dd3e022d644 · outbound

This paper cites Balinsky, W.

An optimal fractional Hardy inequality on the discrete half-line Balinsky, W

Reference 5

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 4de62ee0-8290-4965-93fd-b38c521d5c64 · outbound

This paper cites Sharp Poincaré-Hardy and Poincaré- Rellich inequalities on the hyperbolic space.J.

An optimal fractional Hardy inequality on the discrete half-line Sharp Poincaré-Hardy and Poincaré- Rellich inequalities on the hyperbolic space.J

Reference 6

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Observation 706ac49b-05ba-4e0a-a44f-421f93163fd8 · outbound

This paper cites On the spectrum of singular boundary-value problems.Mat.

An optimal fractional Hardy inequality on the discrete half-line On the spectrum of singular boundary-value problems.Mat

Reference 7

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Observation 43277f0e-358a-4398-977a-d07b0e8c9417 · outbound

This paper cites The best constant in a fractional Hardy inequality.

An optimal fractional Hardy inequality on the discrete half-line The best constant in a fractional Hardy inequality

Reference 8

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Observation c6e142e5-603a-4089-8240-05ac3baf9994 · outbound

This paper cites Hardy’s inequality and Green function on metric measure spaces.J.

An optimal fractional Hardy inequality on the discrete half-line Hardy’s inequality and Green function on metric measure spaces.J

Reference 9

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Observation a58ca1cb-5cc5-46f2-aeba-4941d588ef28 · outbound

This paper cites Hardy’s inequality for the fractional powers of a discrete Lapla- cian.

An optimal fractional Hardy inequality on the discrete half-line Hardy’s inequality for the fractional powers of a discrete Lapla- cian

Reference 10

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Observation 8285b7fe-8665-4dfb-9016-e22173e1e04e · outbound

This paper cites On Landis conjecture for positive Schrödinger operators on graphs.Int.

An optimal fractional Hardy inequality on the discrete half-line On Landis conjecture for positive Schrödinger operators on graphs.Int

Reference 11

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Observation 06acdabb-c1d6-4148-9df7-c65e50e0bace · outbound

This paper cites The space of Hardy-weights for quasilinear operators on discrete graphs.

An optimal fractional Hardy inequality on the discrete half-line The space of Hardy-weights for quasilinear operators on discrete graphs

Reference 12

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Observation 7a56be24-537c-41b8-a78c-9a8b3bb50bf2 · outbound

This paper cites The Landis conjecture via Liouville comparison principle and criticality theory.

An optimal fractional Hardy inequality on the discrete half-line The Landis conjecture via Liouville comparison principle and criticality theory

Reference 13

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Observation d9118d4e-6656-4620-846d-8b8d4930d2fb · outbound

This paper cites On existence of minimizers for weighted $L^p$-Hardy inequalities on $C^{1,\gamma}$-domains with compact boundary.

An optimal fractional Hardy inequality on the discrete half-line On existence of minimizers for weighted $L^p$-Hardy inequalities on $C^{1,\gamma}$-domains with compact boundary

Reference 14

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Observation 1b27123d-4ffb-403f-9949-5aa4ebac6e09 · outbound

This paper cites Optimal Hardy weight for second-order elliptic operator: an answer to a problem of Agmon.J.

An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy weight for second-order elliptic operator: an answer to a problem of Agmon.J

Reference 15

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Observation 1cdf5db1-8628-4e6a-972d-752bac5f5bf7 · outbound

This paper cites OptimalLp Hardy-type inequalities.

An optimal fractional Hardy inequality on the discrete half-line OptimalLp Hardy-type inequalities

Reference 16

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Observation ba5e9513-eb0f-4199-b129-d8cd3a05ac5f · outbound

This paper cites Fractional and non-fractional Hardy inequality on a lattice $\Z^d$.

An optimal fractional Hardy inequality on the discrete half-line Fractional and non-fractional Hardy inequality on a lattice $\Z^d$

Reference 17

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Observation ae6081df-c14b-48bc-b90b-317bd9f783b2 · outbound

This paper cites On(global)uniquecontinuation properties of the fractional discrete Laplacian.J.

An optimal fractional Hardy inequality on the discrete half-line On(global)uniquecontinuation properties of the fractional discrete Laplacian.J

Reference 18

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Observation 22858bda-1eb4-4220-b758-d98cf47669ff · outbound

This paper cites Landis' conjecture: a survey.

An optimal fractional Hardy inequality on the discrete half-line Landis' conjecture: a survey

Reference 19

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Observation e04dfda3-ea17-41f0-ba1c-8e6988ccafe3 · outbound

This paper cites On the optimality and decay ofp-Hardy weights on graphs.Calc.

An optimal fractional Hardy inequality on the discrete half-line On the optimality and decay ofp-Hardy weights on graphs.Calc

Reference 20

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Observation 0bc3ca9b-aa78-42ad-8a36-70b0e900d1a1 · outbound

This paper cites Quasi-Linear Criticality Theory and Green's Functions on Graphs.

An optimal fractional Hardy inequality on the discrete half-line Quasi-Linear Criticality Theory and Green's Functions on Graphs

Reference 21

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Observation 05fe2f86-85f6-4047-87ac-3f5e66fe1c67 · outbound

This paper cites An improved discretep-Hardy inequal- ity.

An optimal fractional Hardy inequality on the discrete half-line An improved discretep-Hardy inequal- ity

Reference 22

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Observation d480df2e-3a4f-4105-9a81-2fb7d466ccdf · outbound

This paper cites Sharp Hardy-type inequalities for non-compact har- monic manifolds and Damek–Ricci spaces.Israel J.

An optimal fractional Hardy inequality on the discrete half-line Sharp Hardy-type inequalities for non-compact har- monic manifolds and Damek–Ricci spaces.Israel J

Reference 23

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Observation 0f3f34bd-06be-40a2-9843-af39f42de05c · outbound

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An optimal fractional Hardy inequality on the discrete half-line Optimal Poincar\'e-Hardy-type Inequalities on Manifolds and Graphs

Reference 24

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An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work

Reference 25

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An optimal fractional Hardy inequality on the discrete half-line Frank, Elliott H

Reference 26

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Observation 632b056b-35e4-4f4b-ba58-6e52f4cf51aa · outbound

This paper cites Criticality transition for positive powers of the discrete Laplacian on the half line.Rev.

An optimal fractional Hardy inequality on the discrete half-line Criticality transition for positive powers of the discrete Laplacian on the half line.Rev

Reference 27

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Observation d86b64b5-cb32-4600-a6c2-4b4554b2a927 · outbound

This paper cites An improved discrete Rellich inequality on the half-line.

An optimal fractional Hardy inequality on the discrete half-line An improved discrete Rellich inequality on the half-line

Reference 28

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Observation 04088e08-8ee5-470a-87a8-b0e584557a09 · outbound

This paper cites Hardy and Rellich inequality on lattices.

An optimal fractional Hardy inequality on the discrete half-line Hardy and Rellich inequality on lattices

Reference 29

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Observation 9ece4995-2b9e-44aa-a86e-5f2a7f212e62 · outbound

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An optimal fractional Hardy inequality on the discrete half-line One-dimensional discrete Hardy and Rellich inequalities on integers

Reference 30

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Observation 64552b91-cbf9-4bc7-9796-dca416319e7c · outbound

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An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work

Reference 31

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Observation bc1958b8-2ba0-4f91-b61c-f909ae887931 · outbound

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An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work

Reference 32

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Observation f1c500d9-f2aa-40cf-9a3a-6c65bd9c3e01 · outbound

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An optimal fractional Hardy inequality on the discrete half-line Wojciechowski.Graphs and discrete Dirichlet spaces

Reference 33

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Observation 895e8cc1-c0ef-4349-a84f-0c7a1da7213f · outbound

This paper cites Optimal Hardy inequality for fractional Laplacians on the integers.Ann.

An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy inequality for fractional Laplacians on the integers.Ann

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Observation 3443c2c9-b62f-4cab-a2dc-ce5c09326f58 · outbound

This paper cites An improved discrete Hardy in- equality.

An optimal fractional Hardy inequality on the discrete half-line An improved discrete Hardy in- equality

Reference 35

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:33.770762Z digest=sha256:dfb591e4bedcfd142d7c2a411e97451a59f3292057afaca3e0478826ce7cd53c

Observation c1ac30a8-433a-4e89-a874-49a301ce25d9 · outbound

This paper cites Optimal Hardy inequalities for Schrödinger operators on graphs.Comm.

An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy inequalities for Schrödinger operators on graphs.Comm

Reference 36

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raw_fallback, observed 2026-08-06T19:13:42.176767Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:33.905860Z digest=sha256:f932584ec1239bc137d337e7180a9ae8082e270424693491b05555a5ec76ebf3

Observation 2ffe1db3-3419-438a-beec-ab0c51714791 · outbound

This paper cites Criticality theory for Schrödinger operators on graphs.J.

An optimal fractional Hardy inequality on the discrete half-line Criticality theory for Schrödinger operators on graphs.J

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:42.009488Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:34.072499Z digest=sha256:947f82218c709c9d84a046773f5a176b3ff93f9a03b51e30b3cba515605edc95

Observation 7daa7e33-9a03-419f-90c6-cd813bbc286a · outbound

This paper cites From Hardy to Rellich inequalities on graphs.

An optimal fractional Hardy inequality on the discrete half-line From Hardy to Rellich inequalities on graphs

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:41.868846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:34.248501Z digest=sha256:bc68a35c559b51081f8d528270749d6e410ba98e6dfda3655d2af222762cb325

Observation 4a77a96c-67dc-473c-a5f1-226b9e608208 · outbound

This paper cites an unresolved cited work.

An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:13:41.721785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:34.413513Z digest=sha256:08a5e0efd2147c2306a28c1572d6b414f9a0be0485f6d66de2b0ebe431b6340a

Observation 34a72ea6-22a2-4f79-9743-b248dda5d46f · outbound

This paper cites Geometrical aspects of spectral theory.

An optimal fractional Hardy inequality on the discrete half-line Geometrical aspects of spectral theory

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:41.461483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:34.697200Z digest=sha256:236ddca36905889fd671c5a1a933963aec71d7c9cda3a8b9b08e0ab102105621

Observation 0aa027e1-4dec-46c4-82c0-304df6c09d40 · outbound

This paper cites A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality.Amer.

An optimal fractional Hardy inequality on the discrete half-line A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality.Amer

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:41.314744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:34.885475Z digest=sha256:60f9b96b336f9590eb29115c78b17d979cec2c4c78af376a73c5861271cb96b7

Observation 9c78fc55-ab16-46fc-adee-25dcc982d827 · outbound

This paper cites Spectral enclosures and stability for non- self-adjoint discrete Schrödinger operators on the half-line.Bull.

An optimal fractional Hardy inequality on the discrete half-line Spectral enclosures and stability for non- self-adjoint discrete Schrödinger operators on the half-line.Bull

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:41.187820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.018939Z digest=sha256:4045cae8221653d5e94ae697113649f83652e51f8e24d9a8112bb25487d40f5e

Observation 25c9489d-8966-46fb-b07b-2278b99203ae · outbound

This paper cites The prehistory of the Hardy inequality.

An optimal fractional Hardy inequality on the discrete half-line The prehistory of the Hardy inequality

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:41.054255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.179791Z digest=sha256:3372028818eb2a22e51a996781ef00529566174010335f8b5eaedafeed769962

Observation 79ea6c32-754a-4c01-81cd-73d93037bb48 · outbound

This paper cites Hölder-Lebesgue regularity and almost periodicity for semidis- crete equations with a fractional Laplacian.

An optimal fractional Hardy inequality on the discrete half-line Hölder-Lebesgue regularity and almost periodicity for semidis- crete equations with a fractional Laplacian

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:40.863154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.269807Z digest=sha256:06042e0cbc0f2a00a7b00ce3a8ea29d28e8ff5ee0adb099aba5620ce57739654

Observation 07ff939b-d9f1-4640-a615-b5cc1a98d714 · outbound

This paper cites Cambridge Series in Statistical and Proba- bilistic Mathematics.

An optimal fractional Hardy inequality on the discrete half-line Cambridge Series in Statistical and Proba- bilistic Mathematics

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:40.661314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.327965Z digest=sha256:695adcc1f0d80bd675d0b0f3f837e5f8e8233b741be835ab50a0e2cb9821660d

Observation b036d28e-b541-4e37-9770-f2dde9c642fd · outbound

This paper cites A Liouville-type theorem for Schrödinger operators.Comm.

An optimal fractional Hardy inequality on the discrete half-line A Liouville-type theorem for Schrödinger operators.Comm

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:40.225075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.412971Z digest=sha256:f019334149a13a1b73bd4712bcd63b61adc1990ecec1d6aeaf1c0860c14619f3

Observation 79208bc4-a08f-4a6c-85f8-9a455c689853 · outbound

This paper cites On positive solutions of the(p, A)-Laplacian with potential in Morrey space.Anal.

An optimal fractional Hardy inequality on the discrete half-line On positive solutions of the(p, A)-Laplacian with potential in Morrey space.Anal

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:39.893327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.514951Z digest=sha256:c874a8ab9f15edaa0d461ab61b43214a0948e921855be792165180b29beec4b6

Observation 70a816e7-fa85-4712-92a0-fa5ca83693ff · outbound

This paper cites Ground state alternative forp-Laplacian with potential term.

An optimal fractional Hardy inequality on the discrete half-line Ground state alternative forp-Laplacian with potential term

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:39.522011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.601695Z digest=sha256:3f2bde64beb2e7c47d3edbfec19ab387ab490534c78a377a246acfccfef2ac91

Observation 13f2bb16-154c-427a-a345-af7773d82698 · outbound

This paper cites ImprovementofthediscreteHardyinequality.

An optimal fractional Hardy inequality on the discrete half-line ImprovementofthediscreteHardyinequality

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:39.099325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.677837Z digest=sha256:fa5602a63d485f896d038698975496cc497bdf844b4e67af979bcab8d7286d6d

Observation 9958a3e7-2ffa-40dc-a722-e32cd8c79735 · outbound

This paper cites (Weak) Hardy and Poincaré inequalities and criticality theory.

An optimal fractional Hardy inequality on the discrete half-line (Weak) Hardy and Poincaré inequalities and criticality theory

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:38.779212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.789676Z digest=sha256:cd1025a81329b4296086153bbf83bccf3334f66e2ad80b9d7797e3543a132272

Observation c9bd9f10-cc75-4790-af82-3babb52267a4 · outbound

This paper cites Orthogonal polynomials, volume Vol.

An optimal fractional Hardy inequality on the discrete half-line Orthogonal polynomials, volume Vol

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:38.505535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.878880Z digest=sha256:ddce8770c915a4282da0059b293f18e6d2ad4df85cec51c5c2195dc50ba8c25a

Observation 9f89ee1e-5b34-49b8-8ff1-ca50bff3b4b4 · outbound

This paper cites Criticality for Schrödinger type operators based on recurrent symmetric stable processes.

An optimal fractional Hardy inequality on the discrete half-line Criticality for Schrödinger type operators based on recurrent symmetric stable processes

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:38.110282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:35.949421Z digest=sha256:2a20f92a23342c3173fdeb577177e06fe557c5fcb66ffdeead16394269208eb7

Observation 96b98785-c12e-4432-a05f-a4814aa33758 · outbound

This paper cites Optimal Hardy-weights for the (p, A)-Laplacian with a potential term.

An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy-weights for the (p, A)-Laplacian with a potential term

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:37.786911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:36.029823Z digest=sha256:a5ac1d84a9103c5124813d0a69fae722a230fdd3e4a6bd4f716dc34b0698df3a

Observation 7e1d5bde-20b3-455c-b618-b79f7a8379bb · outbound

This paper cites Nauk SSSR, Vsesoyuz.

An optimal fractional Hardy inequality on the discrete half-line Nauk SSSR, Vsesoyuz

Reference 220

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:13:41.590842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-06T19:13:34.566758Z digest=sha256:c9d7225bb7e8b5e52fa3813f5d40679915a4ab31299034394532a785afaaf7cb

Pith citing papers

No inbound Pith citation observations are available.