Pith. sign in

Paper Citation Record · LEDGER

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues

As of 17 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2506.16378.

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

pith.paper-citation-record.v1
2506.16378 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:37:31.531275Z

measured 32 of 32 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T15:52:32.848879Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

31 of 31 outbound references displayed

  • verified exact1
  • verified fuzzy22
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c5df658b-f3f2-4070-83ce-9cf5b81a00a1 · outbound

This paper cites The Lp-boundedness of wave operators for 4th order Schr¨ odinger operators on R2, I, preprint 2025, arXiv:2504.11753.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues The Lp-boundedness of wave operators for 4th order Schr¨ odinger operators on R2, I, preprint 2025, arXiv:2504.11753

Reference 1

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verified exact
raw_fallback, observed 2026-08-15T19:37:31.702549Z

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.

source=pdf_text observed=2026-08-15T19:37:31.397433Z digest=sha256:67677674934077cac27331a7b0b49bad6cd5770e305f2352d7bd0cabbb054d86

Observation 4f0f5806-9600-4dba-bce2-72bcc0d2f33c · outbound

This paper cites The Lp-boundedness of wave operators for fourth order Schr¨ odinger operators on R4.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues The Lp-boundedness of wave operators for fourth order Schr¨ odinger operators on R4

Reference 2

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raw_fallback, observed 2026-08-15T19:37:32.277979Z

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.

source=pdf_text observed=2026-08-15T19:37:31.402951Z digest=sha256:6c45821c0f6f067fe2b6e410eec9129c3b271fe5976a315f8ae55d9e5415e5a4

Observation 249099e8-16cc-4eba-8ad6-3c8bbd5c3669 · outbound

This paper cites The $L^p$-boundedness of wave operators for higher order Schr\"odinger operator with zero singularities in low odd dimensions.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues The $L^p$-boundedness of wave operators for higher order Schr\"odinger operator with zero singularities in low odd dimensions

Reference 3

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unresolved
no resolver link, observed 2026-08-15T19:37:31.407954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:37:31.407954Z digest=sha256:d207fe21c849b8b3b59fdb7d97c0217bbe8d501850efbae4c04497b81ff9eb43

Observation dda1bb1e-975e-42a1-84ea-5332edb3fc4b · outbound

This paper cites Agmon, Spectral properties of Schr¨ odinger operators and scattering theory.Ann.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Agmon, Spectral properties of Schr¨ odinger operators and scattering theory.Ann

Reference 4

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verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.250575Z

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.

source=pdf_text observed=2026-08-15T19:37:31.412769Z digest=sha256:1085ecc2df5ac12b004337e15cb0cb53002f978b4576c3228937f335e9affdd9

Observation 1cd5bc3c-8e70-4bcd-a8f0-3f92e8f69417 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 5

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raw_fallback, observed 2026-08-15T19:37:32.230255Z

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.

source=pdf_text observed=2026-08-15T19:37:31.417840Z digest=sha256:ee8f259fa4f2df841a816089e216fcb4e30b0327b8e278930c7dc1b87632ecc9

Observation d8dfb834-379b-4524-a850-a670652ff2d4 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 6

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raw_fallback, observed 2026-08-15T19:37:32.207716Z

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.

source=pdf_text observed=2026-08-15T19:37:31.421954Z digest=sha256:b1a0ec307dd15a9d7770e62ec32b9c1eb01eb992ad1f377115817b7fec4a3b4d

Observation c0b18c1c-2168-4893-a572-c015b070807e · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 7

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raw_fallback, observed 2026-08-15T19:37:32.157263Z

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.

source=pdf_text observed=2026-08-15T19:37:31.426621Z digest=sha256:1c932ec6652cd3e411a528008383d723b06cb6f69641a6d4582b08a6b24690aa

Observation 3b6e5099-f86c-47ae-a053-b1fabff7fa13 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 8

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raw_fallback, observed 2026-08-15T19:37:32.137610Z

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.

source=pdf_text observed=2026-08-15T19:37:31.430826Z digest=sha256:949c488556017963ca16947606443969b24d9a6cc4b22b457e2e7d7af87692f5

Observation 3fa0af78-a2ca-4c0e-ae42-a8e813e62d63 · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:37:32.118631Z

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.

source=pdf_text observed=2026-08-15T19:37:31.434475Z digest=sha256:ab792a3d74b94677b77c59d29c636a0f4cf1b1b582eb5af421892fce0e0ab04e

Observation 3a5d2027-ee93-487e-a2b5-73ae255b2aa6 · outbound

This paper cites Finco, and K.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Finco, and K

Reference 10

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verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.094114Z

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.

source=pdf_text observed=2026-08-15T19:37:31.438171Z digest=sha256:4a6e0e3bddc56096584a62d0f417cb8301b4734dc0e2c6d22305021d992d675f

Observation 3e9eeec2-bd98-4641-a21d-88a11ef9a8eb · outbound

This paper cites Galtbayar, and K.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Galtbayar, and K

Reference 11

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verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.075335Z

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.

source=pdf_text observed=2026-08-15T19:37:31.442116Z digest=sha256:d142fa89f250030596f380711a03f0bb70242663c3a0580f7b4e77ecf65adadf

Observation be46135d-0cde-4293-a5f5-87b3dc7c5b7a · outbound

This paper cites Goldberg and W.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Goldberg and W

Reference 12

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verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.056185Z

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.

source=pdf_text observed=2026-08-15T19:37:31.446864Z digest=sha256:b3bf1aa5d8a6a615de8eb2d81d0168eb428aa319603cdd9c73673281a2b0e0b4

Observation 1c5bb21b-2f3f-43c5-bb22-3d420768d20e · outbound

This paper cites Goldberg and W.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Goldberg and W

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.036244Z

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.

source=pdf_text observed=2026-08-15T19:37:31.451337Z digest=sha256:360c21d1bfa6ef0420e37aabe85607548931956dba62899f182c3465841769b6

Observation 4fd53239-3fdf-4473-85db-4b385118f4ab · outbound

This paper cites Goldberg, and W.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Goldberg, and W

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:32.014994Z

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.

source=pdf_text observed=2026-08-15T19:37:31.456070Z digest=sha256:a8af31352d4969ed866e8f73e00cc71fba64dbbe629269ebcdb4aa052f19ec40

Observation 6ec90b21-001a-44a4-8dc2-293bfd384a8f · outbound

This paper cites H¨ ormander,The existence of wave operators in scattering theory.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues H¨ ormander,The existence of wave operators in scattering theory

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.997091Z

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.

source=pdf_text observed=2026-08-15T19:37:31.460579Z digest=sha256:5daf9c97c4497f24641e92c2a2fca70ae284dcce217e71e0c232757796a52218

Observation 5479812e-55c9-4702-aef4-33d49b78fe93 · outbound

This paper cites Jensen, and G.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Jensen, and G

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.976753Z

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.

source=pdf_text observed=2026-08-15T19:37:31.464490Z digest=sha256:236c1fbcb51a84f734399e3cee7da4ae0d1767a2d4c98112d797224cd6aec3f8

Observation 1ef8725c-a614-4403-be6b-c09f79bc014a · outbound

This paper cites Jensen and K.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Jensen and K

Reference 17

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raw_fallback, observed 2026-08-15T19:37:31.961721Z

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.

source=pdf_text observed=2026-08-15T19:37:31.467763Z digest=sha256:38692001346a9f22ae8e3ff7b4651048c358f66754501cb9dfab9fd1edb2dfa4

Observation b07d2536-22b6-4797-84e4-cb6d818deee3 · outbound

This paper cites Mizutani, Z.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Mizutani, Z

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.945006Z

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.

source=pdf_text observed=2026-08-15T19:37:31.471615Z digest=sha256:f9947ccf2cb35a06cf809c95e7ce84b0cbf55c523a1b863df47a82725bd95797

Observation 84e420c7-ce00-461a-abb6-82b6b6aa944d · outbound

This paper cites Mizutani, Z.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Mizutani, Z

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.926022Z

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.

source=pdf_text observed=2026-08-15T19:37:31.476529Z digest=sha256:c213751a1c808473b3a9c851cc4eadd357b89515ad37f4067835d75375f2cd30

Observation a59e7619-3682-41cc-a69f-298e185a422d · outbound

This paper cites Mizutani, Z.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Mizutani, Z

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.909914Z

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.

source=pdf_text observed=2026-08-15T19:37:31.480704Z digest=sha256:03fc02a5e3409aba424b7ac3cfbc9d686b9bf930323d18b0be56b3ffcb182f25

Observation b9aa20ec-1a84-43ed-a1f1-d15fe114a12f · outbound

This paper cites Reed and B.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Reed and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.891199Z

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.

source=pdf_text observed=2026-08-15T19:37:31.486159Z digest=sha256:de0e25ccfa59ac199a41be222a7733daf33a87620ca84acb1cad9cf2e7ae17b3

Observation 6deb1edf-cb79-400f-bd3e-a15ea0c631b4 · outbound

This paper cites Schechter, Scattering theory for pseudodifferential operators, Quart.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Schechter, Scattering theory for pseudodifferential operators, Quart

Reference 22

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verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.875205Z

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.

source=pdf_text observed=2026-08-15T19:37:31.490275Z digest=sha256:7076da260c8e8a0d16e7035a2ad737e185d0cd1853d7c7f9475e92aa905c8eae

Observation f63ec354-1057-47c3-93e1-d3cb9100f122 · outbound

This paper cites Schechter, Scattering theory for elliptic operators of arbitrary order.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Schechter, Scattering theory for elliptic operators of arbitrary order

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.856602Z

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.

source=pdf_text observed=2026-08-15T19:37:31.495239Z digest=sha256:140992b0dd9d7b5a2fe1997791112898ba8f13308ed79318d0ff556f40cba061

Observation 77b125e4-3521-4a94-b2ae-35db290b3e9b · outbound

This paper cites Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.J.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.J

Reference 24

Resolution
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raw_fallback, observed 2026-08-15T19:37:31.836730Z

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.

source=pdf_text observed=2026-08-15T19:37:31.500166Z digest=sha256:f82a55e67210cf1909e389eb0717ee57e9afbc6dd203104b1bfb8d075f66d774

Observation c0e1527d-456d-4119-98bb-dd4061a214b3 · outbound

This paper cites Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.818852Z

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.

source=pdf_text observed=2026-08-15T19:37:31.504050Z digest=sha256:f0a3380f4cdeef6f855bcdb15dfd01aac2c27d96d152e30c68e3fddbd59b57f3

Observation bec6a9d5-fb3b-4f65-888e-2fd9c83957d8 · outbound

This paper cites Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Wk,p-continuity of wave operators for Schr¨ odinger operators

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.798531Z

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.

source=pdf_text observed=2026-08-15T19:37:31.508680Z digest=sha256:7294a1ce9e376f8b0c74cd8096a5b40f6b28611e1e8445187da01e4dd1efdef8

Observation ade1c6ab-5f28-472d-b14d-620c6626ba93 · outbound

This paper cites Yajima, The Lp boundedness of wave operators for Schr¨ odinger operators with threshold singularities I.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, The Lp boundedness of wave operators for Schr¨ odinger operators with threshold singularities I

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.778789Z

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.

source=pdf_text observed=2026-08-15T19:37:31.513090Z digest=sha256:86eda28fefdca7e0aee360004c90d531f1eabdd1430790608be187b90188b1af

Observation a1013de0-53e5-4720-ac38-4823759cdb4a · outbound

This paper cites Wave Operators for Schr\"odinger Operators with Threshold Singuralities, Revisited.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Wave Operators for Schr\"odinger Operators with Threshold Singuralities, Revisited

Reference 28

Resolution
unresolved
no resolver link, observed 2026-08-15T19:37:31.516897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:37:31.516897Z digest=sha256:3b7ee3bbaddc1aedda68f0d6a58fcb6b9be9748a7d467ef54030882785218cd8

Observation 0bf1ab00-837a-4dd6-9204-492f45a1f7e7 · outbound

This paper cites Yajima, Remark on theLp-boundedness of wave operators for Schr¨ odinger operators with threshold singularities, Documenta Mathematica 21 (2016), 391–443.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Yajima, Remark on theLp-boundedness of wave operators for Schr¨ odinger operators with threshold singularities, Documenta Mathematica 21 (2016), 391–443

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.762282Z

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.

source=pdf_text observed=2026-08-15T19:37:31.522022Z digest=sha256:e8540910318c432e9a1fd53f7ef055c4ab03238e7036f826b25960f6ef4f901b

Observation 12b62085-5411-4ab8-8098-bd800917fab6 · outbound

This paper cites L1 and L∞-boundedness of wave operators for three dimensional Schr¨ odinger operators with threshold singularities, Tokyo J.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues L1 and L∞-boundedness of wave operators for three dimensional Schr¨ odinger operators with threshold singularities, Tokyo J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:37:31.743688Z

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.

source=pdf_text observed=2026-08-15T19:37:31.526755Z digest=sha256:5a242ab3095c434262bfda78d2a1d9b907c33342e615020ce2a5dc4949b6b8f0

Observation 234b5f08-f038-475c-ae9e-22832bb6843a · outbound

This paper cites an unresolved cited work.

$L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:37:31.724638Z

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.

source=pdf_text observed=2026-08-15T19:37:31.531275Z digest=sha256:f295a6eff46fd4c8b96e09413cf558dd4b3f0381c9800b70565dc3cd06ea041e

Pith citing papers

Observation 61ba3b79-c896-4dd1-a61f-413d5e5c0b9c · inbound

The $L^p$-continuity of wave operators for fractional order Schr\"odinger operators cites this paper.

The $L^p$-continuity of wave operators for fractional order Schr\"odinger operators $L^p$ boundedness of wave operators for higher order schr\"odinger operators with threshold eigenvalues

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-04T15:52:32.848879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T15:52:32.848879Z digest=sha256:68070bbdc6000cd5cc636c41657b388f81e083033797baf7ab0530527c7dd3fd