Paper Citation Record · LEDGER

Entropy numbers of classes defined by integral operators

As of 16 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 1 inbound Pith citation observation for arXiv:2505.08572.

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

pith.paper-citation-record.v1
2505.08572 v2

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T22:06:10.310348Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T00:45:35.590550Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

44 of 44 outbound references displayed

verified exact1
verified fuzzy37
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 41561a16-3a9c-4121-bb84-a300f01f006d · outbound

This paper cites Babadzhanov and V.M.

Entropy numbers of classes defined by integral operators Babadzhanov and V.M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.980863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6dc19d43-0af8-469e-ba7e-52581ad19a15 · outbound

This paper cites Babenko, On the approximation of periodic functions of several variables by trigonometric polynomials, Dokl.

Entropy numbers of classes defined by integral operators Babenko, On the approximation of periodic functions of several variables by trigonometric polynomials, Dokl

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.965760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 62d1d8e5-4080-4195-a315-2608ed05b16f · outbound

This paper cites Belinsky, Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative, J.

Entropy numbers of classes defined by integral operators Belinsky, Estimates of entropy numbers and Gaussian measures for classes of functions with bounded mixed derivative, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.950415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6f489e4c-9569-4c86-af8d-09258131a1bc · outbound

This paper cites Birman and M.Z.

Entropy numbers of classes defined by integral operators Birman and M.Z

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.936476Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6db36c22-3440-4f6f-8839-f79bbb3e710b · outbound

This paper cites Carl, Entropy numbers, s-numbers, and eigenvalue problems, J.

Entropy numbers of classes defined by integral operators Carl, Entropy numbers, s-numbers, and eigenvalue problems, J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.922186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 14ac7a0b-0481-4dab-b51d-fa4d2f426803 · outbound

This paper cites Dissertation (1985), Moscow, MGU.

Entropy numbers of classes defined by integral operators Dissertation (1985), Moscow, MGU

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.907012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7494891c-263e-44ca-8aca-91932b39c2f5 · outbound

This paper cites Hyperbolic Cross Approximation.

Entropy numbers of classes defined by integral operators Hyperbolic Cross Approximation

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T22:06:10.142764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66ea8c3a-e8d5-4de2-b411-bab2d1fda27e · outbound

This paper cites Galeev, Approximation of classes of functions with several bounded derivatives by Fourier sums, Matem.

Entropy numbers of classes defined by integral operators Galeev, Approximation of classes of functions with several bounded derivatives by Fourier sums, Matem

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.892578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7a5e46c1-e81d-4571-8365-7bba567727e2 · outbound

This paper cites Galeev, Kolmogorov widths of the classes W ¯α p and H ¯α p of peri- odic functions of several variables in the space Lq, Izv.

Entropy numbers of classes defined by integral operators Galeev, Kolmogorov widths of the classes W ¯α p and H ¯α p of peri- odic functions of several variables in the space Lq, Izv

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.878560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c270c4d3-3eb7-4448-8051-a303d47b1431 · outbound

This paper cites Gluskin, On a problem concerning widths, Dokl.

Entropy numbers of classes defined by integral operators Gluskin, On a problem concerning widths, Dokl

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.864889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 40355863-5d1c-4580-9515-3d902bc42f73 · outbound

This paper cites Ismagilov, Widths of sets in normed linear spaces and the ap- proximation of functions by trigonometric polynomials, Uspekhi Mat.

Entropy numbers of classes defined by integral operators Ismagilov, Widths of sets in normed linear spaces and the ap- proximation of functions by trigonometric polynomials, Uspekhi Mat

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.851075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 470c6a94-5d0e-4a34-9b46-fc3e54cb0888 · outbound

This paper cites Kashin, Widths of certain finite-dimensional sets and classes of smooth functions, Izv.

Entropy numbers of classes defined by integral operators Kashin, Widths of certain finite-dimensional sets and classes of smooth functions, Izv

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.836947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0a79bd9d-8128-4ec2-b05a-1201c880b19c · outbound

This paper cites Kashin and V.N.

Entropy numbers of classes defined by integral operators Kashin and V.N

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.822721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 923a5dc2-3476-4163-8da7-526295036766 · outbound

This paper cites Kashin and V.N.

Entropy numbers of classes defined by integral operators Kashin and V.N

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.807998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b535c6dc-e149-47d7-8217-33cb538957d0 · outbound

This paper cites Kolmogorov, Uber die beste Ann¨ aherung von Funktionen einer Funktionklasse, Ann.

Entropy numbers of classes defined by integral operators Kolmogorov, Uber die beste Ann¨ aherung von Funktionen einer Funktionklasse, Ann

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.793930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 71537903-7ad7-4fd5-89bd-0a0346af0c5c · outbound

This paper cites Kolmogorov, On certain asymptotic characteristics of of some completely bounded metric spaces, Dokl.

Entropy numbers of classes defined by integral operators Kolmogorov, On certain asymptotic characteristics of of some completely bounded metric spaces, Dokl

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.779697Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4f109e11-0713-497e-917a-b5be5f30a6b5 · outbound

This paper cites Kolmogorov and V.M.

Entropy numbers of classes defined by integral operators Kolmogorov and V.M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.765144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 626f9a43-9ebb-4359-b1e0-986426195556 · outbound

This paper cites Kuelbs and W.V.

Entropy numbers of classes defined by integral operators Kuelbs and W.V

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.750266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 91a66f7f-23c6-426a-9c27-4e8a94ff3d8f · outbound

This paper cites Lorentz, M.v.

Entropy numbers of classes defined by integral operators Lorentz, M.v

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.735802Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ec2bcbb6-6ea3-4131-ab1b-beea139b7def · outbound

This paper cites an unresolved cited work.

Entropy numbers of classes defined by integral operators Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T22:06:10.721745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cb54f97f-a8fc-4198-95d1-8bf05ddb7f71 · outbound

This paper cites Mityagin, Approximation of functions in the spaces Lp andC on the torus, Mat.

Entropy numbers of classes defined by integral operators Mityagin, Approximation of functions in the spaces Lp andC on the torus, Mat

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.708069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ad4554c1-7f86-48ae-9348-2f29217560c5 · outbound

This paper cites Rudin, Some theorems on Fourier coefficients, Proc.

Entropy numbers of classes defined by integral operators Rudin, Some theorems on Fourier coefficients, Proc

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.693873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 394a74bb-b564-4866-98ce-cc688256cdac · outbound

This paper cites Sch¨ utt, Entropy numbers of diagonal operators between symmetric Banach spaces, J.

Entropy numbers of classes defined by integral operators Sch¨ utt, Entropy numbers of diagonal operators between symmetric Banach spaces, J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.679674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3e61972b-556d-4a59-8e70-c2b369df1633 · outbound

This paper cites Smolyak, The ϵ-entropy of the classesEαk s (B) andWα s (B) in the metric L2, Dokl.

Entropy numbers of classes defined by integral operators Smolyak, The ϵ-entropy of the classesEαk s (B) andWα s (B) in the metric L2, Dokl

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.665670Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f3461f19-ff63-49d2-971d-24bff05b04fa · outbound

This paper cites an unresolved cited work.

Entropy numbers of classes defined by integral operators Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-15T22:06:10.651455Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 34580470-7b5e-49d7-951e-fbe090c59031 · outbound

This paper cites Talagrand, The small ball problem for the Brownian sheet, Ann.

Entropy numbers of classes defined by integral operators Talagrand, The small ball problem for the Brownian sheet, Ann

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.637604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 431e1b33-7f91-4c35-a587-a54e8f451792 · outbound

This paper cites Temlyakov, On the approximation of periodic functions of sev- eral variables with bounded mixed difference, Dokl.

Entropy numbers of classes defined by integral operators Temlyakov, On the approximation of periodic functions of sev- eral variables with bounded mixed difference, Dokl

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.623259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8f7c80d3-95aa-4a82-9dc4-1cca83cfdec6 · outbound

This paper cites Temlyakov, Widths of some classes of functions of several vari- ables, Dokl.

Entropy numbers of classes defined by integral operators Temlyakov, Widths of some classes of functions of several vari- ables, Dokl

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.609389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f2fcae4a-1fea-4628-94f1-bc7dc129daf5 · outbound

This paper cites Temlyakov, Approximation of functions with a bounded mixed difference by trigonometric polynomials and the widths of some classes of functions, Izv.

Entropy numbers of classes defined by integral operators Temlyakov, Approximation of functions with a bounded mixed difference by trigonometric polynomials and the widths of some classes of functions, Izv

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.594830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c659800d-b2d4-4462-8e5c-62986eab7560 · outbound

This paper cites Temlyakov, Approximation of periodic functions of several vari- ables by trigonometric polynomials, and widths of some classes of functions, Izv.

Entropy numbers of classes defined by integral operators Temlyakov, Approximation of periodic functions of several vari- ables by trigonometric polynomials, and widths of some classes of functions, Izv

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.579329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 24735b06-9376-4fdc-8b2a-b4a4af91d4a6 · outbound

This paper cites Temlyakov, On best bilinear approximations of periodic func- tions of several variables, Dokl.

Entropy numbers of classes defined by integral operators Temlyakov, On best bilinear approximations of periodic func- tions of several variables, Dokl

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.562522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8af966ec-8668-4f79-ae04-4f02e79533fb · outbound

This paper cites Temlyakov, On widths of function classes, Dokl.

Entropy numbers of classes defined by integral operators Temlyakov, On widths of function classes, Dokl

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.547039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c99e22bb-7019-46af-9f2b-9cf5809bd9e7 · outbound

This paper cites Temlyakov, On estimates of ϵ-entropy and widths of classes of functions with bounded mixed derivative or difference, Dokl.

Entropy numbers of classes defined by integral operators Temlyakov, On estimates of ϵ-entropy and widths of classes of functions with bounded mixed derivative or difference, Dokl

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.531963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a7e5f823-9675-4e2d-a218-aece18c1d8a5 · outbound

This paper cites Temlyakov, Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference, Trudy Matem.

Entropy numbers of classes defined by integral operators Temlyakov, Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference, Trudy Matem

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.516867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c3cd3666-fdf4-4724-9d0a-2b75b7aad608 · outbound

This paper cites Temlyakov, Estimates of the best bilinear approximations of functions of two variables and some of their applications, Mat.

Entropy numbers of classes defined by integral operators Temlyakov, Estimates of the best bilinear approximations of functions of two variables and some of their applications, Mat

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.502123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3d4c0f38-7b16-4347-8cb4-ed69132b850c · outbound

This paper cites Temlyakov, Approximation of functions with bounded mixed derivative, Trudy MIAN, 178 (1986), 1–112.

Entropy numbers of classes defined by integral operators Temlyakov, Approximation of functions with bounded mixed derivative, Trudy MIAN, 178 (1986), 1–112

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T22:06:10.275001Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b5099e9-550b-400d-84a7-b25d5667fae8 · outbound

This paper cites Temlyakov, Bilinear approximation and related questions, Trudy MIAN im.

Entropy numbers of classes defined by integral operators Temlyakov, Bilinear approximation and related questions, Trudy MIAN im

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.478394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 191fef1b-2d5c-418f-a740-39c919bfc452 · outbound

This paper cites Temlyakov, An inequality for trigonometric polynomials and its application for estimating the entropy numbers, J.

Entropy numbers of classes defined by integral operators Temlyakov, An inequality for trigonometric polynomials and its application for estimating the entropy numbers, J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.460734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fc1ac09c-a09c-4454-88be-09ee9a7b1154 · outbound

This paper cites Temlyakov, On two problems in the multivariate approximation, East J.

Entropy numbers of classes defined by integral operators Temlyakov, On two problems in the multivariate approximation, East J

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.444305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 882decef-25af-46b4-a554-a3beb9509df6 · outbound

This paper cites Temlyakov, Greedy Approximation, Cambridge University Press, 2011.

Entropy numbers of classes defined by integral operators Temlyakov, Greedy Approximation, Cambridge University Press, 2011

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T22:06:10.292251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2b45d72-ba9b-4f29-8a9a-1dd24439a788 · outbound

This paper cites Temlyakov, On the entropy numbers of the mixed smoothness func- tion classes, Journal of Approximation Theory, 217 (2017), 26–56.

Entropy numbers of classes defined by integral operators Temlyakov, On the entropy numbers of the mixed smoothness func- tion classes, Journal of Approximation Theory, 217 (2017), 26–56

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.415095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c956c5e2-c1fa-4c14-83ab-53c87b525be2 · outbound

This paper cites Temlyakov, Multivariate Approximation , Cambridge University Press, 2018.

Entropy numbers of classes defined by integral operators Temlyakov, Multivariate Approximation , Cambridge University Press, 2018

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T22:06:10.301244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34fefc48-be50-46af-9f8d-d6a3eed3754d · outbound

This paper cites Brief introduction in greedy approximation.

Entropy numbers of classes defined by integral operators Brief introduction in greedy approximation

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-15T22:06:10.355944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c9af1dc8-8ae6-4d03-af04-2cc9b6bbb045 · outbound

This paper cites Tikhomirov, Some questions of approximation theory, Moscow State University, 1976 (in Russian).

Entropy numbers of classes defined by integral operators Tikhomirov, Some questions of approximation theory, Moscow State University, 1976 (in Russian)

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:06:10.389410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 3d7f5c6e-0dc1-477a-a74e-652e83d82daa · inbound

Nonlinear approximation with adaptive dictionaries cites this paper.

Nonlinear approximation with adaptive dictionaries Entropy numbers of classes defined by integral operators

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-14T00:45:35.590550Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.