On degree of approximation function classes in the space Lebesgue with anisotropic norm
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 5-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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There is the anisotropic space Lebesgue of periodic function in the paper. In the paper is obtained the estimate degree of approximation O. V. Besov's classes in anisotropic space Lebesgue by trigonometric polynomials with harmonics in hyperbolic crosses.
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G. Akishev. On degree of approximation function classes in the space Lebesgue with anisotropic norm. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 5-17. http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a0/

[1] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, M., 1977, 456 pp. | MR

[2] Amanov T. I., Prostranstva differentsiruemykh funktsii s dominiruyuschei smeshannoi proizvodnoi, Alma-ata, 1976, 224 pp. | MR

[3] Babenko K. I., “O priblizhenii odnogo klassa periodicheskikh funktsii mnogikh peremennykh trigonometricheskimi mnogochlenami”, Dokl. AN SSSR, 132:5 (1960), 982–985 | MR | Zbl

[4] Telyakovskii S. A., “Nekotorye otsenki dlya trigonometricheskikh ryadov s kvazivypuklymi koeffitsientami”, Matem. sb., 63 (1964), 426–444

[5] Mityagin B. S., “Priblizhenie funktsii v prostranstvakh $L^p$ i $C$ na tore”, Matem. sb., 58:3 (1962), 397–414 | Zbl

[6] Bugrov Ya. S., “Priblizhenie klassov funktsii s dominiruyuschei smeshannoi proizvodnoi”, Matem. sb., 64 (1964), 410–418 | MR | Zbl

[7] Nikolskaya N. S., “Priblizhenie differentsiruemykh funktsii mnogikh peremennykh summami Fure v metrike $L_p$”, Sib. matem. zhurn., 15:2 (1974), 395–412

[8] Galeev E. M., Matem. zametki, 23:2 (1978), 197–212 | MR | Zbl

[9] Galeev E. M., “Poperechniki po Kolmogorovu klassov periodicheskikh funktsii mnogikh peremennykh $W_p^r$ i $H_p^r$ v prostranstve $L_q$”, Izv. AN SSSR. Ser. Matem., 49:5 (1985), 916–934 | MR | Zbl

[10] Temlyakov V. N., “Priblizhenie periodicheskikh funktsii neskolkikh peremennykh s ogranichennoi smeshannoi raznostyu”, Matem. sb., 113:1 (1980), 65–80 | MR | Zbl

[11] Temlyakov V. N., “Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi”, Tr. MIAN SSSR, 178, 1986, 3–112 | MR

[12] Kashin B. S., Temlyakov V. N., “Ob odnoi norme i approksimatsionnykh kharakteristikakh klassov funktsii mnogikh peremennykh”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, M., 1999, 69–99 | MR

[13] Din Zung, “Priblizhenie funktsii mnogikh peremennykh na tore trigonometricheskimi polinomami”, Matem. sb., 131:2 (1986), 251–271 | Zbl

[14] Pustovoitov N. N., “Priblizhenie mnogomernykh funktsii s zadannoi mazhorantoi smeshannykh modulei nepreryvnosti”, Matem. zametki, 65 (1999), 107–117 | DOI | MR | Zbl

[15] Romanyuk A. S., “Priblizhenie klassov Besova periodicheskikh funktsii mnogikh peremennykh v prostranstve $L_q$”, Ukr. matem. zhurn., 43 (1991), 1398–1408 | MR | Zbl

[16] Romanyuk A. S., “Priblizhenie klassov periodicheskikh funktsii mnogikh peremennykh”, Matem. zametki, 71:1 (2002), 109–121 | DOI | MR | Zbl

[17] Akishev G., “Otsenka poryadka priblizheniya klassov Besova trigonometricheskimi polinomami”, Vestn. Karagand. un-ta. Ser. Matematika, 2004, no. 3, 9–16

[18] Akishev G., “O priblizhenii funktsionalnykh klassov v prostranstvakh so smeshannoi normoi”, Matem. zhurn., 5 (2005), 5–15 | MR | Zbl

[19] Besov O. V., “Teorema Litlvuda-Peli dlya smeshannoi normoi”, Tr. MIAN SSSR, 170, 1984, 31–36 | MR | Zbl

[20] Potapov M. K., “Teoremy vlozheniya smeshannoi metrike”, Tr. MIAN SSSR, 156, 1980, 143–156 | MR | Zbl