Geodesic
The embedding and approximation of classes of functions with a~dominant mixed difference
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2009), pp. 83-86.

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

We obtain a criterion for embedding the class SHpΩ into that SBq,θΩ∗ (1). We also determine the exact order of the best approximations of functions from classes SBp,θΩ by trigonometric polynomials whose harmonics belong to sets generated by level surfaces of the majorant Λ(t).
Mots-clés : Besov's spases, embedding theorem, modulus of continuity, best approximations. 
@article{IVM_2009_8_a10,
     author = {M. B. Sikhov},
     title = {The embedding and approximation of classes of functions with a~dominant mixed difference},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--86},
     publisher = {mathdoc},
     number = {8},
     year = {2009},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/IVM_2009_8_a10/}
}
TY  - JOUR
AU  - M. B. Sikhov
TI  - The embedding and approximation of classes of functions with a~dominant mixed difference
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 83
EP  - 86
IS  - 8
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/IVM_2009_8_a10/
LA  - ru
ID  - IVM_2009_8_a10
ER  - 
%0 Journal Article
%A M. B. Sikhov
%T The embedding and approximation of classes of functions with a~dominant mixed difference
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 83-86
%N 8
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/IVM_2009_8_a10/
%G ru
%F IVM_2009_8_a10
M. B. Sikhov. The embedding and approximation of classes of functions with a~dominant mixed difference. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2009), pp. 83-86. https://geodesic-test.mathdoc.fr/item/IVM_2009_8_a10/

[1] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. MMO, 5, 1956, 483–522 | MR | Zbl

[2] Ulyanov P. L., “O modulyakh nepreryvnosti i koeffitsientakh Fure”, Vestn. MGU. Ser. matem., mekh., 1995, no. 1, 37–52 | MR

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

[4] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975, 480 pp. | MR | Zbl

[5] Amanov T. I., Prostranstva differentsiruemykh funktsii s dominiruyuschei smeshannoi proizvodnoi, Almaty, 1976, 224 pp. | MR

[6] Din Zung, “Priblizhenie funktsii mnogikh peremennykh na tore trigonometricheskimi polinomami”, Matem. sb., 131(173):2 (1986), 251–271 | MR | Zbl

[7] Pustovoitov N N., “Predstavlenie i priblizhenie periodicheskikh funktsii mnogikh peremennykh s zadannym smeshannym modulem nepreryvnosti”, Anal. Math., 20 (1994), 35–48 | DOI | MR | Zbl

[8] Ulyanov P. L., “Vlozhenie nekotorykh klassov funktsii $H_p^\omega$”, Izv. AN SSSR. Ser. matem., 32:3 (1968), 649–686 | MR | Zbl

[9] Sun Yongsheng, Wang Heping, “Reprezentation and approximation of multivariate periodic functions with bounded mixed moduli of smoothness”, Tr. MIAN, 219, 1997, 356–377 | MR | Zbl