Approximation to the Sobolev classes $W_q^r$ of functions of several variables by bilinear forms in $L_p$ for $2\le q\le p\le\infty$
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 18-34 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classes $W_q^r$ by bilinear forms in $L_p$ for $2 \le q \le p \le\infty$ is found.
@article{MZM_1997_62_1_a2,
     author = {M. Babayev},
     title = {Approximation to the {Sobolev} classes $W_q^r$ of functions of several variables by bilinear forms in $L_p$ for $2\le q\le p\le\infty$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {18--34},
     year = {1997},
     volume = {62},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a2/}
}
TY  - JOUR
AU  - M. Babayev
TI  - Approximation to the Sobolev classes $W_q^r$ of functions of several variables by bilinear forms in $L_p$ for $2\le q\le p\le\infty$
JO  - Matematičeskie zametki
PY  - 1997
SP  - 18
EP  - 34
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a2/
LA  - ru
ID  - MZM_1997_62_1_a2
ER  - 
%0 Journal Article
%A M. Babayev
%T Approximation to the Sobolev classes $W_q^r$ of functions of several variables by bilinear forms in $L_p$ for $2\le q\le p\le\infty$
%J Matematičeskie zametki
%D 1997
%P 18-34
%V 62
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a2/
%G ru
%F MZM_1997_62_1_a2
M. Babayev. Approximation to the Sobolev classes $W_q^r$ of functions of several variables by bilinear forms in $L_p$ for $2\le q\le p\le\infty$. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 18-34. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a2/

[1] Schmidt E., “Zur Theorie der linearen und nicht linearen Integralgleichungen, I”, Math. Ann., 63 (1906/07), 433–476 | DOI

[2] Temlyakov V. N., “Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi”, Tr. MIAN, 178, Nauka, M., 1986, 3–113 | MR | Zbl

[3] Temlyakov V. N., “O nailuchshikh bilineinykh priblizheniyakh periodicheskikh funktsii mnogikh peremennykh”, Dokl. AN SSSR, 2:2 (1986), 301–304 | MR

[4] Temlyakov V. N., “Bilineinaya approksimatsiya i prilozheniya”, Tr. MIAN, 187, Nauka, M., 1989, 191–215 | MR

[5] Babaev M.-B. A., “Priblizhenie sobolevskikh klassov funktsii summami proizvedenii funktsii menshego chisla peremennykh i kvazipoperechniki”, Dokl. AN AzSSR, 1986, no. 3, 3–5 | Zbl

[6] Babaev M.-B. A., “O poryadke priblizheniya sobolevskogo klassa bilineinymi formami v $L_p$ pri $1\le q\le p\le2$”, Matem. sb., 182:1 (1991), 122–129

[7] Babaev M.-B. A., “O poryadke priblizheniya sobolevskogo klassa $W_q^r$ bilineinymi formami v $L_p$ pri $1\le q\le2\le p\le\infty$”, Tr. MIRAN, 198, Nauka, M., 1992, 21–40 | Zbl

[8] Akhiezer N. I., Lektsii po teorii approksimatsii, Fizmatgiz, M., 1965

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

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

[11] Birman M. Sh., Solomyak M. Z., “Kusochno-polinomialnye priblizheniya funktsii klassov $W_p^\alpha$”, Matem. sb., 73 (115) (1967), 331–355 | MR | Zbl

[12] Maiorov V. E., Predstavleniya i nailuchshee priblizhenie na klassakh funktsii mnogikh peremennykh, Diss. ... k. f.-m. n., MISI, M., 1976

[13] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960