Geodesic
Estimation of error of cubature formula in Besov space
Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 147-156 
E. S. Smailov; N. T. Tleukhanova. Estimation of error of cubature formula in Besov space. Eurasian mathematical journal, Tome 1 (2010) no. 1, pp. 147-156. http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a11/
@article{EMJ_2010_1_1_a11,
     author = {E. S. Smailov and N. T. Tleukhanova},
     title = {Estimation of error of cubature formula in {Besov} space},
     journal = {Eurasian mathematical journal},
     pages = {147--156},
     year = {2010},
     volume = {1},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a11/}
}
TY  - JOUR
AU  - E. S. Smailov
AU  - N. T. Tleukhanova
TI  - Estimation of error of cubature formula in Besov space
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 147
EP  - 156
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a11/
LA  - en
ID  - EMJ_2010_1_1_a11
ER  - 
%0 Journal Article
%A E. S. Smailov
%A N. T. Tleukhanova
%T Estimation of error of cubature formula in Besov space
%J Eurasian mathematical journal
%D 2010
%P 147-156
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_1_a11/
%G en
%F EMJ_2010_1_1_a11

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

In this paper estimates of the error of a cubature formula in Besov classes are obtained. The method of research is essentially based on the choice of a Lizorkin system.

[1] N. S. Bakhvalov, “On approximate calculation of multiple integrals”, Vestnik Moskov. Univ. Ser. I. Mat. Mekh., 4 (1959), 3–18 (in Russian) | MR

[2] K. K. Frolov, “Upper error bounds for quadrature formulas on function classes”, Doklady Akad. Nauk SSSR, 231:4 (1976), 818–821 (in Russian) | MR | Zbl

[3] N. M. Korobov, Number-theoretic methods in approximate analysis, Fizmatgiz, Moscow, 1963 (in Russian) | Zbl

[4] P. I. Lizorkin, “Bases and multipliers in the spaces $B_{p\theta}^r(T)$”, Trudy Mat. Inst. Steklov, 143, 1977, 88–104 (in Russian) | MR | Zbl

[5] P. I. Lizorkin, S. M. Nikol'skii, “Functional spaces of mixed smoothness from decompositional point of view”, Trudy Mat. Inst. Steklov, 187, 1989, 143–161 (in Russian) | MR

[6] E. Nursultanov, N. Tleukhanova, “On the approximate computation of integrals for functions in the spaces $W_p^\alpha$”, Uspekhi Mat. Nauk, 55:6 (2000), 153–154 (in Russian) | DOI | MR | Zbl

[7] E. Nursultanov, N. Tleukhanova, “Quadrature formula for classes of functions of low smoothness”, Matem. Sb., 194:10 (2003), 133–160 (in Russian) | DOI | MR | Zbl

[8] I. F. Sharygin, “Lower error estimates for quadrature formulae on function classes”, Zh. Vychisl. Mat. Mat. Fiz., 3 (1963), 370–376 (in Russian) | MR | Zbl

[9] V. N. Temlyakov, “Approximate recovery of periodic functions of several variables”, Matem. Sb., 128:2 (1985), 256–268 (in Russian) | MR | Zbl

[10] V. N. Temlyakov, “On the approximate reconstruction of periodic functions of several variables”, Doklady Akad. Nauk SSSR, 280:6 (1985), 1310–1313 (in Russian) | MR | Zbl