, of the classes $B^r_{1,\theta}$ and $B^r_{\infty,\theta}$ and also of the trigonometric widths of the classes $B^r_{p,\theta}$ in $L_q$ for $p$ and $q$ satisfying certain relations are obtained. Bibliography: 18 titles.
@article{SM_2006_197_1_a4,
author = {A. S. Romanyuk},
title = {Kolmogorov and trigonometric widths of the {Besov} classes $B^r_{p,\theta}$ of multivariate periodic functions},
journal = {Sbornik. Mathematics},
pages = {69--93},
year = {2006},
volume = {197},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2006_197_1_a4/}
}
TY - JOUR
AU - A. S. Romanyuk
TI - Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions
JO - Sbornik. Mathematics
PY - 2006
SP - 69
EP - 93
VL - 197
IS - 1
UR - http://geodesic.mathdoc.fr/item/SM_2006_197_1_a4/
LA - en
ID - SM_2006_197_1_a4
ER -
A. S. Romanyuk. Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions. Sbornik. Mathematics, Tome 197 (2006) no. 1, pp. 69-93. http://geodesic.mathdoc.fr/item/SM_2006_197_1_a4/
[1] A. S. Romanyuk, “Priblizhenie klassov Besova periodicheskikh funktsii mnogikh peremennykh v prostranstve $L_q$”, Ukr. matem. zhurn., 43:10 (1991), 1398–1408 | MR | Zbl
[2] A. S. Romanyuk, “O nailuchshikh trigonometricheskikh priblizheniyakh i kolmogorovskikh poperechnikakh klassov Besova funktsii mnogikh peremennykh”, Ukr. matem. zhurn., 45:5 (1993), 663–675 | MR | Zbl
[3] E. M. Galeev, “Poperechniki klassov Besova $B_{p,\theta}^r(\mathbb T^d)$”, Matem. zametki, 69:5 (2001), 656–665 | MR | Zbl
[4] O. V. Besov, “O nekotorom semeistve funktsionalnykh prostranstv. Teoremy vlozheniya i prodolzheniya”, Dokl. AN SSSR, 126:6 (1959), 1163–1165 | MR | Zbl
[5] V. N. Temlyakov, “Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi”, Trudy MIAN, 178, 1986, 3–113 | MR | Zbl
[6] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR
[7] P. I. Lizorkin, S. M. Nikolskii, “Prostranstva funktsii smeshannoi gladkosti s dekompozitsionnoi tochki zreniya”, Trudy MIAN, 187, 1989, 143–161 | MR
[8] S. M. Nikolskii, “Neravenstva dlya tselykh funktsii konechnoi stepeni i ikh primenenie v teorii differentsiruemykh funktsii mnogikh peremennykh”, Trudy MIAN, 38, 1951, 244–278
[9] D. Jakson, “Certain problem of closest approximation”, Bull. Amer. Math. Soc. (2), 39:12 (1933), 889–906 | DOI
[10] E. Schmidt, “Zur Theorie der linearen und nichtlinearen Integralgleichungen. I”, Math. Ann., 63 (1907), 433–476 | DOI | MR | Zbl
[11] V. N. Temlyakov, “Otsenki asimptoticheskikh kharakteristik klassov funktsii s ogranichennoi smeshannoi proizvodnoi ili raznostyu”, Trudy MIAN, 189, 1988, 138–168 | MR
[12] B. S. Kashin, V. N. Temlyakov, “O nailuchshikh $m$-chlennykh priblizheniyakh i entropii mnozhestv v prostranstve $L^1$”, Matem. zametki, 56:5 (1994), 57–86 | MR | Zbl
[13] R. S. Ismagilov, “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, UMN, 29:3 (1974), 161–178 | MR | Zbl
[14] E. S. Belinskii, E. M. Galeev, “O naimenshei velichine norm smeshannykh proizvodnykh trigonometricheskikh polinomov s zadannym chislom garmonik”, Vestn. MGU. Ser. 1. Matem., mekh., 1991, no. 2, 3–7 | MR | Zbl
[15] G. Khardi, D. Littlvud, G. Polia, Neravenstva, IL, M., 1948
[16] A. Zigmund, Trigonometricheskie ryady, t. 2, Mir, M., 1965 | MR
[17] E. S. Belinskii, “Priblizhenie periodicheskikh funktsii mnogikh peremennykh “plavayuschei” sistemoi eksponent i trigonometricheskie poperechniki”, Dokl. AN SSSR, 284:6 (1985), 1294–1297 | MR | Zbl
[18] A. S. Romanyuk, “Nailuchshie $M$-chlennye trigonometricheskie priblizheniya klassov Besova periodicheskikh funktsii mnogikh peremennykh”, Izv. RAN. Ser. matem., 67:2 (2003), 61–100 | MR | Zbl