Geodesic
On the Error of Multidimensional Quadrature Formulas for Certain Classes of Functions
Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 433-439.

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We obtain regular (with respect to the power scale) estimates of the errors of multidimensional optimal quadrature formulas in spaces of periodic functions with constraints on Fourier coefficients in the $\ell_p$-norm for $1$.
Mots-clés : optimal quadrature formula, Fourier coefficient
Keywords: space of periodic functions, Korobov grid, Frolov grid, Hölder's inequality. 
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M. A. Romanov. On the Error of Multidimensional Quadrature Formulas for Certain Classes of Functions. Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 433-439. http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a10/

[1] K. K. Frolov, Kvadraturnye formuly na klassakh funktsii, Dis. $\dots$ kand. fiz.-matem. nauk, VTs AN SSSR, M., 1979

[2] M. M. Skriganov, “Constructions of uniform distributions in terms of geometry of numbers”, Algebra i analiz, 6:3 (1994), 200–230 | MR | Zbl

[3] V. A. Bykovskii, Otsenki otklonenii optimalnykh setok v $L_p$-norme i teoriya kvadraturnykh formul, IPM DVO RAN, Vladivostok–Khabarovsk, 1995

[4] V. N. Temlyakov, “Ob odnom prieme polucheniya otsenok snizu pogreshnostei kvadraturnykh formul”, Matem. sb., 181:10 (1990), 1403–1413 | MR | Zbl

[5] N. M. Korobov, “O priblizhennom vychislenii kratnykh integralov s pomoschyu metodov teorii chisel”, Dokl. AN SSSR, 115:6 (1957), 1062–1065 | MR | Zbl

[6] N. S. Bakhvalov, “O priblizhennom vychislenii kratnykh integralov”, Vestn. Mosk. un-ta. Ser. Matem., mekh., astron., fiz., khim., 1959, no. 4, 3–18 | MR

[7] I. F. Sharygin, “Otsenki snizu pogreshnosti kvadraturnykh formul na klassakh funktsii”, ZhVM i MF, 3 (1963), 370–376 | MR | Zbl

[8] V. F. Lev, O kvadraturnykh formulakh dlya klassov s ogranicheniyami na koeffitsienty Fure, dep. v VINITI 6294–V87

[9] V. A. Bykovskii, O pravilnom poryadke pogreshnosti optimalnykh kubaturnykh formul v prostranstvakh s dominiruyuschei proizvodnoi i kvadratichnykh otkloneniyakh setok, DVNTs AN SSSR, Vladivostok, 1985

[10] V. A. Bykovskii, M. A. Romanov, “Kvadraturnyi fazovyi perekhod”, Dokl. RAN, 416:6 (2007), 727–731 | MR | Zbl

[11] S. A. Smolyak, “Kvadraturnye i interpolyatsionnye formuly na tenzornykh proizvedeniyakh nekotorykh klassov funktsii”, Dokl. AN SSSR, 148:5 (1963), 1042–1045 | MR | Zbl

[12] V. A. Bykovskii, Teoretiko-chislovye reshetki v evklidovykh prostranstvakh i ikh prilozheniya, Dis. $\dots$ dokt. fiz.-matem. nauk, KhO IPM DVO RAN, Khabarovsk, 1989