Paper Citation Record · LEDGER

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential

As of 18 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2607.07171.

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

pith.paper-citation-record.v1
2607.07171 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-10T19:48:39.761787Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

verified exact0
verified fuzzy14
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d72a4be6-0a34-4104-b797-726e4d66c859 · outbound

This paper cites 137, Springer, New York, 2001.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential 137, Springer, New York, 2001

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.477690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e16a44fc-902f-4cd6-afe9-ee1ebb77efdd · outbound

This paper cites A.,The heat equation with a singular potential, Transactions of the American Mathematical Society284(1984), no.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential A.,The heat equation with a singular potential, Transactions of the American Mathematical Society284(1984), no

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.479442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation db4ddf05-4897-4e6c-927b-4f72e0456fe5 · outbound

This paper cites Classe di Scienze25(1997), no.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Classe di Scienze25(1997), no

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.481036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 66af3d4c-0c88-483a-b871-2034b2bc934a · outbound

This paper cites an unresolved cited work.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-07-10T19:57:34.472096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ee46ac4d-e5b8-4b21-bf7e-ead1576dc831 · outbound

This paper cites an unresolved cited work.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-07-10T19:57:34.470481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 19bd31fe-2897-4fec-b761-7040bccc932d · outbound

This paper cites W.; Rodriguez-Bernal, A.,Self-similarity in homogeneous stationary and evolution prob- lems, Journal of Evolution Equations23(2023), Paper No.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential W.; Rodriguez-Bernal, A.,Self-similarity in homogeneous stationary and evolution prob- lems, Journal of Evolution Equations23(2023), Paper No

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.473851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5d405ec6-ae33-4d96-8b41-1e312fc29c22 · outbound

This paper cites an unresolved cited work.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-07-10T19:57:34.482583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a7cd3293-92cb-4e46-9656-abcc7de1be60 · outbound

This paper cites N.; Kalf, H.,The Bessel differential equation and the Hankel transform, Journal of Computational and Applied Mathematics208(2007), 3–19.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential N.; Kalf, H.,The Bessel differential equation and the Hankel transform, Journal of Computational and Applied Mathematics208(2007), 3–19

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.484282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4c5d623a-d61f-433c-877c-c05eca80d368 · outbound

This paper cites 1, 237–281.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential 1, 237–281

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.468899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9e56e6f7-a5d2-4570-b7d0-9d5946f6f0b3 · outbound

This paper cites S.; Ryzhik, I.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential S.; Ryzhik, I

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.485885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1678814b-6238-47e7-9282-6a90b73a8115 · outbound

This paper cites M.,The heat kernel of a Schroedinger operator with inverse square potential, Proceedings of the London Mathematical Society115(2017), 381–410.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential M.,The heat kernel of a Schroedinger operator with inverse square potential, Proceedings of the London Mathematical Society115(2017), 381–410

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.464369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2324de27-3488-4dbf-b202-5b651053755c · outbound

This paper cites an unresolved cited work.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-07-10T19:57:34.462645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d339c09e-e7ea-491e-aa1a-428568de16e2 · outbound

This paper cites an unresolved cited work.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-07-10T19:57:34.465853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9da72527-1f29-4eae-a309-dda1733a0aeb · outbound

This paper cites D.; Semenov, Yu.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential D.; Semenov, Yu

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.467409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 95b35e91-df7c-4598-a322-f482b88ce290 · outbound

This paper cites D.; Semenov, Yu.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential D.; Semenov, Yu

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.461059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 3836572c-90c7-4620-bd83-bba962aeb802 · outbound

This paper cites Matematica e Applicazioni16(2005), no.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Matematica e Applicazioni16(2005), no

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.487561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 89aea503-d408-4f76-a009-42623a16638a · outbound

This paper cites an unresolved cited work.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-07-10T19:57:34.489349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 3aff17c5-db1f-48c6-8695-267a1875539b · outbound

This paper cites N.,The Use of Integral Transforms, McGraw-Hill, New York, 1972.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential N.,The Use of Integral Transforms, McGraw-Hill, New York, 1972

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.457441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 933081ac-f7e8-41c0-8e79-37fa4a2de7ad · outbound

This paper cites L.; Zuazua, E.,The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, Journal of Functional Analysis173(2000), 103–153.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential L.; Zuazua, E.,The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, Journal of Functional Analysis173(2000), 103–153

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.459429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ee7d418a-d615-4f07-b7d2-ebaaf8493a78 · outbound

This paper cites N.,A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, 1944.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential N.,A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, 1944

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-10T19:57:34.454956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b41329e4-4335-4ddf-a4c3-e7da6815afee · outbound

This paper cites Asymptotic behavior of scalar convection-diffusion equations.

$L^p$-Asymptotic Profiles for the Heat Equation with a Hardy Potential Asymptotic behavior of scalar convection-diffusion equations

Reference 21

Resolution: metadata mismatch; local_arxiv, observed 2026-07-10T19:57:34.112135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.