B. S. Kashin, “Diameters of some finite-dimensional sets and classes of smooth functions”, Math. USSR-Izv., 11:2 (1977), 317

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Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 2, Pages 317–333
DOI: https://doi.org/10.1070/IM1977v011n02ABEH001719 (Mi im1805)

This article is cited in 382 scientific papers (total in 383 papers)

Diameters of some finite-dimensional sets and classes of smooth functions

B. S. Kashin

English version PDF (563 kB) Citations (383) Russian version article

References:

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DOI: https://doi.org/10.1070/IM1977v011n02ABEH001719

Abstract: Estimates of the diameters of certain sets in the Banach spaces

L^{q} (0, 1)

$L^q(0,1)$ and

l_{q}^{n}

$l_q^n$ are given; in particular, the orders of the diameters

d_{n} (W_{p}^{r}, L^{q})

$d_n(W_p^r,L^q)$ ,

p < q

$p<q$ ,

r > 1

$r>1$ , are completely determined.
Bibliography: 18 titles.

Received: 27.02.1976

Bibliographic databases:

Document Type: Article

UDC: 517.5

MSC: Primary 52A05, 46E30; Secondary 46E15, 52A45, 52A40

Language: English

Original paper language: Russian

Citation: B. S. Kashin, “Diameters of some finite-dimensional sets and classes of smooth functions”, Math. USSR-Izv., 11:2 (1977), 317–333

Citation in format AMSBIB

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\by B.~S.~Kashin

\paper Diameters of some finite-dimensional sets and classes of smooth functions

\jour Math. USSR-Izv.

\yr 1977

\vol 11

\issue 2

\pages 317--333

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Linking options:

https://www.mathnet.ru/eng/im1805

https://doi.org/10.1070/IM1977v011n02ABEH001719

https://www.mathnet.ru/eng/im/v41/i2/p334

This publication is cited in the following 383 articles:

V. M. Bukhshtaber, “Poperechniki Kolmogorova, mnogoobraziya Grassmana i razvertka vremennykh ryadov”, Matem. sb., 216:3 (2025), 49–68
A. A. Vasil'eva, “Estimates for the Kolmogorov widths of an intersection of two balls in a mixed norm”, Sb. Math., 215:1 (2024), 74–89
A. A. Vasil'eva, “Kolmogorov widths of an intersection of a finite family of Sobolev classes”, Izv. Math., 88:1 (2024), 18–42
David Krieg, Peter Kritzer, “Homogeneous algorithms and solvable problems on cones”, Journal of Complexity, 83 (2024), 101840
Antonious M. Girgis, Suhas Diggavi, “Multi-Message Shuffled Privacy in Federated Learning”, IEEE J. Sel. Areas Inf. Theory, 5 (2024), 12
A.A. Vasil'eva, “Kolmogorov widths of an intersection of a family of balls in a mixed norm”, Journal of Approximation Theory, 2024, 106046
S. V. Astashkin, “Sequences of independent functions and structure of rearrangement invariant spaces”, Russian Math. Surveys, 79:3 (2024), 375–457
Qianxi Li, Qiurong Yan, Jiawei Dong, Jia Feng, Jiaxin Wu, Jianzhong Cao, Guangsen Liu, Hao Wang, “Single-pixel imaging based on self-supervised conditional mask classifier-free guidance”, Opt. Express, 32:11 (2024), 18771
A. A. Vasil'eva, “Kolmogorov widths of a Sobolev class with constraints on derivatives in different metrics”, Sb. Math., 215:11 (2024), 1468–1498
A. A. Vasil'eva, “Kolmogorov widths of anisotropic function classes and finite-dimensional balls”, Eurasian Math. J., 15:3 (2024), 88–93
A. A. Vasil'eva, “Kolmogorov Widths of the Intersection of Two Finite-Dimensional Balls in a Mixed Norm”, Math. Notes, 113:4 (2023), 584–586
B. S. Kashin, D. G. Romskii, “An Efficient Algorithm for Decomposing a Vector into Two Vectors with a Small Uniform Norm”, Math. Notes, 114:6 (2023), 1484–1487
A. A. Vasileva, “Kolmogorovskie poperechniki peresecheniya dvukh vesovykh klassov Coboleva na otrezke s odinakovoi gladkostyu”, Tr. IMM UrO RAN, 29, no. 4, 2023, 55–63
Inung Wijayanto, Annisa Humairani, Sugondo Hadiyoso, Achmad Rizal, Dasari Lakshmi Prasanna, Suman Lata Tripathi, “Epileptic seizure detection on a compressed EEG signal using energy measurement”, Biomedical Signal Processing and Control, 85 (2023), 104872
V. D. Milman, “Essay on Kashin's Remarkable 1977 Decomposition Theorem”, Proc. Steklov Inst. Math., 319 (2022), 200–208
V. M. Tikhomirov, “Three Stages in the Development of Approximation Theory”, Proc. Steklov Inst. Math., 319 (2022), 1–12
A. A. Vasil'eva, “Bounds for the Kolmogorov Widths of the Sobolev Weighted Classes with Conditions on the Zero and Highest Derivatives”, Russ. J. Math. Phys., 29:2 (2022), 249
B. Kashin, E. Kosov, I. Limonova, V. Temlyakov, “Sampling discretization and related problems”, J. Complexity, 71 (2022), 101653–55
B. Klartag, V. Milman, Analysis at Large, 2022, 203
A.A. Vasil'eva, “Kolmogorov widths of intersections of finite-dimensional balls”, Journal of Complexity, 72 (2022), 101649

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