Geodesic
Kolmogorov widths of the intersection of two finite-dimensional balls
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2021), pp. 23-29.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper order estimates for the Kolmogorov widths of the intersection of two finite-dimensional balls of different radii in $p_0$ and $p_1$ norms are obtained. This problem naturally appeared when estimating the widths of intersections of function classes, which are defined by constraints on the derivatives of different orders.
Keywords: Kolmogorov widths, intersections of finite-dimensional balls. 
@article{IVM_2021_7_a2,
     author = {A. A. Vasil'eva},
     title = {Kolmogorov widths of the intersection of two finite-dimensional balls},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {23--29},
     publisher = {mathdoc},
     number = {7},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_7_a2/}
}
TY  - JOUR
AU  - A. A. Vasil'eva
TI  - Kolmogorov widths of the intersection of two finite-dimensional balls
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 23
EP  - 29
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_7_a2/
LA  - ru
ID  - IVM_2021_7_a2
ER  - 
%0 Journal Article
%A A. A. Vasil'eva
%T Kolmogorov widths of the intersection of two finite-dimensional balls
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 23-29
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_7_a2/
%G ru
%F IVM_2021_7_a2
A. A. Vasil'eva. Kolmogorov widths of the intersection of two finite-dimensional balls. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2021), pp. 23-29. http://geodesic.mathdoc.fr/item/IVM_2021_7_a2/

[1] Tikhomirov V. M., “Teoriya priblizhenii”, Analiz – $2$, Itogi nauki i tekhniki. Sovremen. probl. matem. Fundament. napravleniya, 14, VINITI AN SSSR, M., 1987, 103–260

[2] Pietsch A., “$s$-numbers of operators in Banach space”, Studia Math., 51 (1974), 201–223 | DOI | MR | Zbl

[3] Stesin M. I., “Aleksandrovskie poperechniki konechnomernykh mnozhestv i klassov gladkikh funktsii”, DAN SSSR, 220:6 (1975), 1278–1281 | MR | Zbl

[4] Kashin B. S., “O poperechnikakh oktaedrov”, UMN, 30:4 (184) (1975), 251–252 | MR | Zbl

[5] Kashin B. S., “Poperechniki nekotorykh konechnomernykh mnozhestv i klassov gladkikh funktsii”, Izv. AN SSSR, ser. mat., 41:2 (1977), 334–351 | MR | Zbl

[6] Gluskin E. D., “O nekotorykh konechnomernykh zadachakh teorii poperechnikov”, Vestn. LGU, 13 (1981), 5–10 | Zbl

[7] Gluskin E. D., “Normy sluchainykh matrits i poperechniki konechnomernykh mnozhestv”, Matem. sb., 120 (162):2 (1983), 180–189 | MR | Zbl

[8] Garnaev A. Yu., Gluskin E. D., “O poperechnikakh evklidovogo shara”, DAN SSSR, 277:5 (1984), 1048–1052 | MR | Zbl

[9] Galeev E. M., “Poperechniki po Kolmogorovu peresecheniya klassov periodicheskikh funktsii i konechnomernykh mnozhestv”, Matem. zametki, 29:5 (1981), 749–760 | MR | Zbl

[10] Galeev E. M., “Poperechniki funktsionalnykh klassov i konechnomernykh mnozhestv”, Vladikavkazsk. matem. zhurn., 13:2 (2011), 3–14 | MR | Zbl

[11] Vasil'eva A. A., Kolmogorov widths of weighted Sobolev classes on a multi-dimensional domain with conditions on the derivatives of order $r$ and zero, arXiv: 2004.06013 | MR

[12] Gluskin E. D., “Peresecheniya kuba s oktaedrom plokho approksimiruyutsya podprostranstvami maloi razmernosti”, Priblizhenie funktsii spetsialnymi klassami operatorov, Mezhvuz. sb. nauchn. tr., Min. pros. RSFSR, Vologodsk. gos. ped. in-t, Vologda, 1987, 35–41 | MR

[13] Malykhin Yu. V., Ryutin K. S., “Proizvedenie oktaedrov plokho priblizhaetsya v metrike $l_{2,1}$”, Matem. zametki, 101:1 (2017), 85–90 | MR | Zbl

[14] Vasil'eva A. A., “Widths of function classes on sets with tree-like structure”, J. Appr. Theory, 192 (2015), 19–59 | DOI | MR

[15] Konyagin S. V., Malykhin Yu. V., Ryutin K. S., “O tochnom vosstanovlenii razrezhennogo vektora po lineinym izmereniyam”, Matem. zametki, 94:1 (2013), 122–129 | Zbl