Geodesic
Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 108-121.

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

We obtain order-sharp estimates of best approximation for the classes $B^\Omega_{p,\theta}$ of periodic functions of several variables by trigonometric polynomials whose spectra are generated by the level surfaces of the function $\Omega(t)$.
Keywords: periodic function of several variables, trigonometric polynomial, level surface, Bari–Stechkin condition, modulus of continuity, Hölder'd inequality.
Mots-clés : Vallée-Poussin kernel 
@article{MZM_2010_87_1_a11,
     author = {S. A. Stasyuk},
     title = {Best {Approximations} of {Periodic} {Functions} of {Several} {Variables} from the {Classes} $B^\Omega_{p,\theta}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {108--121},
     publisher = {mathdoc},
     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a11/}
}
TY  - JOUR
AU  - S. A. Stasyuk
TI  - Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$
JO  - Matematičeskie zametki
PY  - 2010
SP  - 108
EP  - 121
VL  - 87
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a11/
LA  - ru
ID  - MZM_2010_87_1_a11
ER  - 
%0 Journal Article
%A S. A. Stasyuk
%T Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$
%J Matematičeskie zametki
%D 2010
%P 108-121
%V 87
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a11/
%G ru
%F MZM_2010_87_1_a11
S. A. Stasyuk. Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 108-121. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a11/

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

[2] N. N. Pustovoitov, “Priblizhenie mnogomernykh funktsii s zadannoi mazhorantoi smeshannykh modulei nepreryvnosti”, Matem. zametki, 65:1 (1999), 107–117 | MR | Zbl

[3] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR | Zbl

[4] A. Zigmund, Trigonometricheskie ryady, T. 1, 2, Mir, M., 1965 | MR | Zbl

[5] V. N. Temlyakov, Approximation of Periodic Functions, Comput. Math. Anal. Ser., Nova Science Publ., Commack, NY, 1993 | MR | Zbl

[6] S. Yongsheng, W. Heping, “Representation and Approximation of Multivariate Periodic Functions with Bounded Mixed Moduli of Smoothness”, Teoriya priblizhenii. Garmonicheskii analiz, Sbornik statei, posvyaschennyi pamyati professora Sergeya Borisovicha Stechkina, Tr. MIAN, 219, Nauka, M., 1997, 356–377 | MR | Zbl

[7] N. N. Pustovoitov, “Predstavlenie i priblizhenie periodicheskikh funktsii mnogikh peremennykh s zadannym smeshannym modulem nepreryvnosti”, Anal. Math., 20:1 (1994), 35–48 | DOI | MR | Zbl

[8] S. A. Stasyuk, O. V. Fedunik, “Aproksimativni kharakteristiki klasiv $B^\Omega_{p,\theta}$ periodichnikh funktsii bagatokh zminnikh”, Ukr. matem. zhurn., 58:5 (2006), 692–704 | MR | Zbl

[9] P. I. Lizorkin, S. M. Nikolskii, “Prostranstva funktsii smeshannoi gladkosti s dekompozitsionnoi tochki zreniya”, Issledovaniya po teorii differentsiruemykh funktsii mnogikh peremennykh i ee prilozheniyam. Chast 13, Sbornik rabot, Tr. MIAN SSSR, 187, Nauka, M., 1989, 143–161 | MR | Zbl

[10] G. G. Khardi, Dzh. E. Littlvud, G. Polia, Neravenstva, IL, M., 1948 | MR | Zbl

[11] R. S. Ismagilov, “Poperechniki mnozhestv v lineinykh normirovannykh prostranstvakh i priblizhenie funktsii trigonometricheskimi mnogochlenami”, UMN, 29:3 (1974), 161–178 | MR | Zbl

[12] A. S. Romanyuk, “Priblizhenie klassov Besova periodicheskikh funktsii mnogikh peremennykh v prostranstve $L_q$”, Ukr. matem. zhurn., 43:10 (1991), 1398–1408 | MR | Zbl

[13] V. N. Temlyakov, “Otsenki asimptoticheskikh kharakteristik klassov funktsii s ogranichennoi smeshannoi proizvodnoi ili raznostyu”, Sbornik trudov Vsesoyuznoi shkoly po teorii funktsii (Dushanbe, avgust 1986 g.), Tr. MIAN SSSR, 189, Nauka, M., 1989, 138–168 | MR | Zbl

[14] A. S. Romanyuk, “Priblizhenie klassov $B_{p,\theta}^r$ periodicheskikh funktsii mnogikh peremennykh lineinymi metodami i nailuchshie priblizheniya”, Matem. sb., 195:2 (2004), 91–116 | MR | Zbl

[15] A. S. Romanyuk, “Bilineinye i trigonometricheskie priblizheniya klassov Besova $B_{p,\theta}^r$ periodicheskikh funktsii mnogikh peremennykh”, Izv. RAN. Ser. matem., 70:2 (2006), 69–98 | MR | Zbl

[16] S. A. Stasyuk, “Naikraschi nablizhennya, kolmogorovski ta trigonometrichni poperechniki klasiv $B^\Omega_{p,\theta}$ periodichnikh funktsii bagatokh zminnikh”, Ukr. matem. zhurn., 56:11 (2004), 1557–1568 | MR | Zbl

[17] N. N. Pustovoitov, “O priblizhenii i kharakterizatsii periodicheskikh funktsii mnogikh peremennykh, imeyuschikh mazhorantu smeshannykh modulei nepreryvnosti spetsialnogo vida”, Anal. Math., 29:3 (2003), 201–218 | DOI | MR | Zbl