Geodesic
Bernstein width of a class of functions of finite smoothness
Sbornik. Mathematics, Tome 190 (1999) no. 4, pp. 539-560 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A weak asymptotic formula is obtained for the Bernstein $n$-width in the space $L_q(I^d)$ of the class $F_p^{l,\omega }(I^d)$ of functions on the cube $I^d$ such that their generalized partial derivatives up to order $l$ belong to $L_p(I^d)$ and the moduli of continuity in the space $L_p(I^d)$ of all their derivatives of order $l$ are majorized by a fixed modulus of continuity $\omega$. 
@article{SM_1999_190_4_a3,
     author = {S. N. Kudryavtsev},
     title = {Bernstein width of a~class of functions of finite smoothness},
     journal = {Sbornik. Mathematics},
     pages = {539--560},
     year = {1999},
     volume = {190},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_4_a3/}
}
TY  - JOUR
AU  - S. N. Kudryavtsev
TI  - Bernstein width of a class of functions of finite smoothness
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 539
EP  - 560
VL  - 190
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_4_a3/
LA  - en
ID  - SM_1999_190_4_a3
ER  - 
%0 Journal Article
%A S. N. Kudryavtsev
%T Bernstein width of a class of functions of finite smoothness
%J Sbornik. Mathematics
%D 1999
%P 539-560
%V 190
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1999_190_4_a3/
%G en
%F SM_1999_190_4_a3
S. N. Kudryavtsev. Bernstein width of a class of functions of finite smoothness. Sbornik. Mathematics, Tome 190 (1999) no. 4, pp. 539-560. http://geodesic.mathdoc.fr/item/SM_1999_190_4_a3/

[1] Galeev E. M., “Bernstein diameters for the classes of periodic functions of several variables”, Math. Balk. (N.S.), 5 (1991), 229–244 | MR | Zbl

[2] Maiorov V. E., “Diskretizatsiya zadachi o poperechnikakh”, UMN, 30:6 (1975), 179–180 | MR | Zbl

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

[4] Höllig K., Quantitative approximation, Proc. int. Symp. (Bonn 1979), Springer-Verlag, New York, 1980, 163–175 | MR

[5] Galeev E. M., “Poperechniki po Kolmogorovu klassov periodicheskikh funktsii odnoi i neskolkikh peremennykh”, Izv. AN SSSR. Ser. matem., 54:2 (1990), 418–429 | MR

[6] Kitbalyan A. A., “O poperechnikakh neizotropnykh klassov funktsii konechnoi gladkosti”, UMN, 45:1 (1990), 177–178 | MR | Zbl

[7] Kudryavtsev S. N., “Poperechniki klassov gladkikh funktsii”, Izv. RAN. Ser. matem., 59:4 (1995), 81–104 | MR | Zbl

[8] Kudryavtsev S. N., “Vosstanovlenie funktsii vmeste s ikh proizvodnymi po znacheniyam funktsii v zadannom chisle tochek”, Izv. RAN. Ser. matem., 58:6 (1994), 79–104 | MR | Zbl

[9] Sofman L. B., “Poperechniki oktaedrov”, Matem. zametki, 5:4 (1969), 429–436 | MR | Zbl

[10] Pich A., Operatornye idealy, Mir, M., 1982 | MR

[11] Pukhov S. V., Poperechniki mnozhestv v banakhovykh prostranstvakh i funktsionalnykh klassov v prostranstvakh s vesom, Izd-vo MGU, M., 1980

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

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