Paper Citation Record · LEDGER

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere

As of 18 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2507.03451.

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

pith.paper-citation-record.v1
2507.03451 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:19:47.921322Z

measured 42 of 42 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

42 of 42 outbound references displayed

verified exact28
verified fuzzy5
unresolved1
parse uncertain0
malformed identifier8
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d11812e4-aaa2-4e78-ba3b-3521a2e58c10 · outbound

This paper cites an unresolved cited work.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Unresolved cited work

Reference 1

Resolution: verified exact; doi, observed 2026-08-06T20:19:53.235452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 24a734f9-0ce6-4caa-b956-842e9bbd20af · outbound

This paper cites Antoine, P.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Antoine, P

Reference 2

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:19:54.120176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a635996c-dedc-4b4a-a6fd-0b17f7317096 · outbound

This paper cites Antoine, P.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Antoine, P

Reference 3

Resolution: verified exact; doi, observed 2026-08-06T20:19:53.015287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7088ee9e-8491-4d5d-8ae0-4b71f2b2c6d3 · outbound

This paper cites Babiˇ c, M.B.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Babiˇ c, M.B

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:19:55.405265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7e5e346d-3e03-4287-8b8c-2752be3eaa2f · outbound

This paper cites Balaji, G.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Balaji, G

Reference 5

Resolution: verified exact; doi, observed 2026-08-06T20:19:52.814320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6ebcad40-005c-4fd8-aa49-a35f6e76aeae · outbound

This paper cites Bernstein, Spherical singular integrals, monogenic kernels and wavelets on the three– dimensional sphere, Adv.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Bernstein, Spherical singular integrals, monogenic kernels and wavelets on the three– dimensional sphere, Adv

Reference 6

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:19:55.321412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a5fcd4da-5f01-4bf2-ac2b-08d502f52566 · outbound

This paper cites Ebert, S.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Ebert, S

Reference 7

Resolution: verified exact; doi, observed 2026-08-06T20:19:52.552530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation de1ce3af-943b-477e-86ef-ee4ab81e6f05 · outbound

This paper cites Edelen, Helmhotz equation on the surface of the unit (N + 1)-sphere, J.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Edelen, Helmhotz equation on the surface of the unit (N + 1)-sphere, J

Reference 8

Resolution: verified exact; doi, observed 2026-08-06T20:19:52.352746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8ae663f6-04ca-4f5a-a1bf-9258b54d7b04 · outbound

This paper cites Fengler, A nonlinear Galerkin scheme involving vectorial and tensorial spherical wavelets for solving the incompressible Navier-Stokes equation on the sphere , PAMM - Proc.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Fengler, A nonlinear Galerkin scheme involving vectorial and tensorial spherical wavelets for solving the incompressible Navier-Stokes equation on the sphere , PAMM - Proc

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T20:19:52.137785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ffa82bbd-59ef-44f6-82eb-84a68e8617be · outbound

This paper cites Frazier, An introduction to wavelets through linear algebra , Springer, New York, 1999, https: //doi.org/10.1007/b97841.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Frazier, An introduction to wavelets through linear algebra , Springer, New York, 1999, https: //doi.org/10.1007/b97841

Reference 10

Resolution: verified exact; doi, observed 2026-08-06T20:19:51.937968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 89361d15-986e-40c7-a48f-7d102cc4f347 · outbound

This paper cites Freeden, T.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Freeden, T

Reference 11

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:19:55.218322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 37500ff9-876a-4b3d-8899-d9c6fa7b5baf · outbound

This paper cites Freeden, M.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Freeden, M

Reference 12

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:19:55.104697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e03f6616-6dba-405a-9270-1e78d720c69d · outbound

This paper cites Freeden, M.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Freeden, M

Reference 13

Resolution: verified exact; doi, observed 2026-08-06T20:19:51.673711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c8add621-223c-4dbb-89be-63fc5eec6972 · outbound

This paper cites Freeden, U.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Freeden, U

Reference 14

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:19:53.875682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b369fe81-d78a-4bee-95ca-cc0072c05550 · outbound

This paper cites Freeden, U.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Freeden, U

Reference 15

Resolution: verified exact; doi, observed 2026-08-06T20:19:51.461760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c21f1001-f23a-4926-86d3-3897435401ee · outbound

This paper cites Gittelson, Adaptive wavelet methods for elliptic partial differential equations with random operators, Numer.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Gittelson, Adaptive wavelet methods for elliptic partial differential equations with random operators, Numer

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:19:54.993495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 50da4477-2228-495d-a1fc-6dad96d1934a · outbound

This paper cites Grebenitcharsky and M.G.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Grebenitcharsky and M.G

Reference 17

Resolution: verified exact; doi, observed 2026-08-06T20:19:51.235822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7e6873b0-2f9f-4811-9476-3dc221b67c85 · outbound

This paper cites Gupta, S.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Gupta, S

Reference 18

Resolution: verified exact; doi, observed 2026-08-06T20:19:50.991811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0fe4f9ec-2752-48c3-adf5-c5ef30504562 · outbound

This paper cites Hajji, S.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Hajji, S

Reference 19

Resolution: verified exact; doi, observed 2026-08-06T20:19:50.742620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation deca5f0e-c30a-4191-a844-5daca1fd4442 · outbound

This paper cites Wavelet-based Methods for Numerical Solutions of Differential Equations.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Wavelet-based Methods for Numerical Solutions of Differential Equations

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:19:53.564150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 822ddf59-484c-4586-bb1f-08f810a9ada1 · outbound

This paper cites Hariharan, K.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Hariharan, K

Reference 21

Resolution: verified exact; doi, observed 2026-08-06T20:19:50.478519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1dd15f0c-2917-45e9-b5f2-ce5c3c168839 · outbound

This paper cites Iglewska-Nowak, A continuous spherical wavelet transform for C(Rn), Appl.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Iglewska-Nowak, A continuous spherical wavelet transform for C(Rn), Appl

Reference 22

Resolution: verified exact; doi, observed 2026-08-06T20:19:50.212174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e1c9b33f-b3a8-47ec-b246-dc43a1fc84c6 · outbound

This paper cites Iglewska-Nowak, Continuous wavelet transforms on n-dimensional spheres , Appl.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Iglewska-Nowak, Continuous wavelet transforms on n-dimensional spheres , Appl

Reference 23

Resolution: verified exact; doi, observed 2026-08-06T20:19:49.989090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4c8477ee-529f-4156-9853-2430153e6b22 · outbound

This paper cites Iglewska-Nowak, Directional wavelets on n-dimensional spheres , Appl.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Iglewska-Nowak, Directional wavelets on n-dimensional spheres , Appl

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T20:19:49.758340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bfd5d20f-de6c-4d8a-b332-aada55d3ca10 · outbound

This paper cites Iglewska-Nowak, Frames of directional wavelets on n–dimensional spheres , Appl.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Iglewska-Nowak, Frames of directional wavelets on n–dimensional spheres , Appl

Reference 25

Resolution: verified exact; doi, observed 2026-08-06T20:19:49.557610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 550d3271-5e7b-4c05-9027-41c2242a0b3b · outbound

This paper cites Iglewska-Nowak, Poisson wavelets on n-dimensional spheres, J.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Iglewska-Nowak, Poisson wavelets on n-dimensional spheres, J

Reference 26

Resolution: verified exact; doi, observed 2026-08-06T20:19:49.317042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3bb4c073-b2dc-4569-bae3-2caf702dcfdc · outbound

This paper cites an unresolved cited work.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Unresolved cited work

Reference 27

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:19:54.889931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cc42de3a-e1f8-4350-bbe9-03fb32c8e612 · outbound

This paper cites Lepik, H.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Lepik, H

Reference 28

Resolution: verified exact; doi, observed 2026-08-06T20:19:49.097630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a9763ae6-dbb9-4151-a3f9-4d66f6bec748 · outbound

This paper cites Mehra, N.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Mehra, N

Reference 29

Resolution: verified exact; doi, observed 2026-08-06T20:19:48.843659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d9eba4a6-2d08-4a89-97a3-9ff56aaab030 · outbound

This paper cites Mei, Q.S.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Mei, Q.S

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:19:54.787728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c20872a0-2c04-4c7c-b713-7870c6d334cd · outbound

This paper cites Michel, Geomathematics – modelling and solving mathematical problems in geodesy and geo- physics, Cambridge University Press, Cambridge, 2022,https://doi.org/10.1017/9781108297882.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Michel, Geomathematics – modelling and solving mathematical problems in geodesy and geo- physics, Cambridge University Press, Cambridge, 2022,https://doi.org/10.1017/9781108297882

Reference 31

Resolution: verified exact; doi, observed 2026-08-06T20:19:48.667518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7aaa1e14-8624-4591-bb7b-e17907b44b9d · outbound

This paper cites Perrier, Towards a method for solving partial differential equations using wavelet bases , Wavelets.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Perrier, Towards a method for solving partial differential equations using wavelet bases , Wavelets

Reference 32

Resolution: verified exact; doi, observed 2026-08-06T20:19:48.534692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7ff1973c-088b-4139-b4ad-278d5c735af1 · outbound

This paper cites Rehman, D.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Rehman, D

Reference 33

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:19:54.698266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ebd0a527-8cc0-4152-bb6c-e0511df2a412 · outbound

This paper cites an unresolved cited work.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Unresolved cited work

Reference 34

Resolution: verified exact; doi, observed 2026-08-06T20:19:48.393768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ac08bcd1-f77d-43b6-9e73-ef2333d4118e · outbound

This paper cites Shimakura, Partial differential operators of elliptic type , Translations of Mathematical Mono- graphs, Vol.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Shimakura, Partial differential operators of elliptic type , Translations of Mathematical Mono- graphs, Vol

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:19:54.614776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8048289e-7c1f-48e9-989e-26c02d406d34 · outbound

This paper cites Szeg¨ o,Orthogonal polynomials, Fourth Edition, AMS Coll.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Szeg¨ o,Orthogonal polynomials, Fourth Edition, AMS Coll

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:19:54.485434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6992b50b-7d5d-4860-99be-067643dc6e34 · outbound

This paper cites Szmytkowski, Closed form of the generalized Green ’s function for the Helmholtz operator on the two-dimensional unit sphere , J.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Szmytkowski, Closed form of the generalized Green ’s function for the Helmholtz operator on the two-dimensional unit sphere , J

Reference 37

Resolution: verified exact; doi, observed 2026-08-06T20:19:48.268568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 12d84257-99ae-4ed4-9b2f-09791ab08fa6 · outbound

This paper cites Szmytkowski, Closed forms of the Green ’s function and the generalized Green ’s function for the Helmholtz operator on the N -dimensional unit sphere , J.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Szmytkowski, Closed forms of the Green ’s function and the generalized Green ’s function for the Helmholtz operator on the N -dimensional unit sphere , J

Reference 38

Resolution: verified exact; doi, observed 2026-08-06T20:19:48.095564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9d7628dc-021f-45d2-95cf-f4ff9762ca69 · outbound

This paper cites Urban, Wavelet methods for elliptic partial differential equations, Numerical Mathematics and Sci- entific Computation.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Urban, Wavelet methods for elliptic partial differential equations, Numerical Mathematics and Sci- entific Computation

Reference 39

Resolution: malformed identifier; no resolver link, observed 2026-08-06T20:19:47.721365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc7e34da-3f9d-4c19-91d2-c85610d8bfbb · outbound

This paper cites an unresolved cited work.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:19:54.345332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5c4ed2e2-f1df-45f7-b0ab-bbe304402475 · outbound

This paper cites an unresolved cited work.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Unresolved cited work

Reference 41

Resolution: malformed identifier; no resolver link, observed 2026-08-06T20:19:47.867918Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95e16584-935d-415c-aa9f-4263d8d56c37 · outbound

This paper cites an unresolved cited work.

Wavelet based solutions to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere Unresolved cited work

Reference 42

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:19:54.238397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.