Paper Citation Record · LEDGER

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets

As of 12 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2412.16621.

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

pith.paper-citation-record.v1
2412.16621 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T10:35:54.137002Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T16:33:55.771823Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

24 of 24 outbound references displayed

verified exact0
verified fuzzy14
unresolved6
parse uncertain4
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6a8f03d8-ded4-417c-ae84-e9685b490e00 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 1

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T10:35:54.324242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 21731a89-0593-4966-bfe6-9d428c0a2fe5 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 2

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T10:35:54.318415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 756831a2-5f39-4b2b-9336-a6138f340f3c · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 3

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T10:35:54.311628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 062cebfc-9ac2-4ce2-9d24-f2c2acdab739 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 4

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T10:35:54.304829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b600cd1c-cb54-4833-92fb-dfade03e6f1d · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:35:54.297982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cfab4d50-c57b-4124-9f4f-74ee807df133 · outbound

This paper cites It is later generalise d to measures, enabling the frequency analysis of distributions.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets It is later generalise d to measures, enabling the frequency analysis of distributions

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.291213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 888cc168-1fd6-4104-8be6-3f6c82797e86 · outbound

This paper cites A few deﬁnitions and propositions are presented before starting the main proof of Theorem 1.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets A few deﬁnitions and propositions are presented before starting the main proof of Theorem 1

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.284386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8c0be5e6-d347-461b-844c-b0c4169ff90c · outbound

This paper cites Let  be a non-empty ﬁnite set.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Let  be a non-empty ﬁnite set

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.277259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 874e9a33-8092-43f8-8b77-bd5102663c38 · outbound

This paper cites By Theorem 2 and the deﬁnition in equation (26), /u1D453(dim /u1D439) = 1.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets By Theorem 2 and the deﬁnition in equation (26), /u1D453(dim /u1D439) = 1

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.270100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 62963a63-2644-4e58-8410-991b68ceb300 · outbound

This paper cites To establish Theorem 4, as an application of Theorem 3, it suﬃces to prove the remaining non-Liouville condition for non-singleton  ⊂ ℕ ⧵ {1}.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets To establish Theorem 4, as an application of Theorem 3, it suﬃces to prove the remaining non-Liouville condition for non-singleton  ⊂ ℕ ⧵ {1}

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.263146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9df32f2a-a51c-4df3-aa84-8452aff0baaf · outbound

This paper cites B/e.sc/r.sc/e.sc/s.sc/n.sc/e.sc/v.sc/i.sc/c.sc/h.sc, F.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets B/e.sc/r.sc/e.sc/s.sc/n.sc/e.sc/v.sc/i.sc/c.sc/h.sc, F

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.255828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e7b80985-528a-4137-aea7-3de66826ec47 · outbound

This paper cites F/e.sc/n.sc/g.sc /a.sc/n.sc/d.sc K./hyphen.scS.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets F/e.sc/n.sc/g.sc /a.sc/n.sc/d.sc K./hyphen.scS

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.249154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 80039f60-407e-4b77-8d74-d0b112e8fa94 · outbound

This paper cites H/e.sc/n.sc/s.sc/l.sc/e.sc/y.sc, The Hausdorﬀ dimensions of some continued fraction Cantor s ets, Journal of Number Theory, 33 (1989), pp.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets H/e.sc/n.sc/s.sc/l.sc/e.sc/y.sc, The Hausdorﬀ dimensions of some continued fraction Cantor s ets, Journal of Number Theory, 33 (1989), pp

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.241973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f0612736-5787-4259-9df3-1323e5032c31 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:35:54.234854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3d3efaa5-6f0b-4b2b-a66c-72015443e046 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:35:54.228203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a51947f3-9108-42b1-a01a-d6520d94a580 · outbound

This paper cites K/a.sc/u.sc/f.sc/m.sc/a.sc/n.sc, Continued fractions and Fourier transforms , Mathematika, 27 (1980), pp.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets K/a.sc/u.sc/f.sc/m.sc/a.sc/n.sc, Continued fractions and Fourier transforms , Mathematika, 27 (1980), pp

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.221583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d8946934-43d8-4ee1-95a3-94f08c226686 · outbound

This paper cites L/i.sc, Decrease of Fourier coeﬃcients of stationary measures , Mathematische Annalen, 372 (2018), pp.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets L/i.sc, Decrease of Fourier coeﬃcients of stationary measures , Mathematische Annalen, 372 (2018), pp

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.214735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5b2eb551-366f-4b83-8116-d2287a78ce52 · outbound

This paper cites L/i.sc /a.sc/n.sc/d.sc T.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets L/i.sc /a.sc/n.sc/d.sc T

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.207345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 446b44a8-3f6c-4e82-a292-4e338a2f6f82 · outbound

This paper cites L/y.sc/o.sc/n.sc/s.sc, The measure of non-normal sets , Inventiones mathematicae, 83 (1986), pp.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets L/y.sc/o.sc/n.sc/s.sc, The measure of non-normal sets , Inventiones mathematicae, 83 (1986), pp

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.199481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 558367cb-d494-4dab-a479-948f4ecb1548 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:35:54.190615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fd011219-1f04-44cf-93ab-d5f3fa98d56a · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:35:54.183072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 602977cb-ddd0-4075-9fbc-23c37d2370b7 · outbound

This paper cites an unresolved cited work.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:35:54.174442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation db56a135-ae6a-4ba6-84bf-d77ef329ca16 · outbound

This paper cites P/o.sc/l.sc/l.sc/i.sc/n.sc/g.sc/t.sc/o.sc/n.sc, S.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets P/o.sc/l.sc/l.sc/i.sc/n.sc/g.sc/t.sc/o.sc/n.sc, S

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.166552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1f2d102d-e2a6-4870-8ee2-d626940668fd · outbound

This paper cites Q/u.sc/e.sc/f.sc/f.sc/eacute.sc/l.sc/e.sc/c.sc /a.sc/n.sc/d.sc O.

Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets Q/u.sc/e.sc/f.sc/f.sc/eacute.sc/l.sc/e.sc/c.sc /a.sc/n.sc/d.sc O

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T10:35:54.158564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 40f837c8-ba62-4ebf-8017-ca775cd06224 · inbound

Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$ cites this paper.

Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than $1/2$ Explicit Upper Bounds on Decay Rates of Fourier Transforms of Self-similar Measures on Self-similar Sets

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T16:33:55.771823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.