Approximation of multidimensional functions with a given majorant of mixed moduli of continuity

被引：12

作者：

Pustovoitov, NN ^{[1
]}

机构：

[1] Moscow State Tech Univ, Moscow, Russia

来源：

MATHEMATICAL NOTES | 1999年 / 65卷 / 1-2期

关键词：

order-exact upper bound; approximation of functions by trigonometric polynomials; mixed modulus of continuity; level surface; hyperbolic cross; Kolmogorov width; Nikol'skii class;

D O I：

10.1007/BF02675013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper order-exact upper bounds for the best approximations of classes H-q(Omega) by trigonometric polynomials are obtained. The spectrum of the approximating polynomials lies in sets generated by the level surfaces of the function Omega(t). These sets are a generalization of hyperbolic crosses to the case of an arbitrary function Omega(t).

引用

页码：89 / 98

页数：10

共 50 条

[1] Approximation of multidimensional functions with a given majorant of mixed moduli of continuity
N. N. Pustovoitov
[J]. Mathematical Notes, 1999, 65 : 89 - 98
[2] Approximation of classes of periodic functions of several variables with given majorant of mixed moduli of continuity
Fedunyk-Yaremchuk, O., V
Hembars'ka, S. B.
[J]. CARPATHIAN MATHEMATICAL PUBLICATIONS, 2021, 13 (03) : 838 - 850
[3] Approximation of classes of periodic functions of several variables with given majorant of mixed moduli of continuity
Fedunyk-Yaremchuk, O., V
Hembars'ka, S. B.
Solich, K., V
[J]. CARPATHIAN MATHEMATICAL PUBLICATIONS, 2023, 15 (02) : 468 - 481
[4] Estimates of the approximation characteristics of the classes Bp,θΩ of periodic functions of several variables with given majorant of mixed moduli of continuity
A. F. Konograi
[J]. Mathematical Notes, 2014, 95 : 656 - 669
[5] Estimates of the approximation characteristics of the classes B p,θ Ω of periodic functions of several variables with given majorant of mixed moduli of continuity
Konograi, A. F.
[J]. MATHEMATICAL NOTES, 2014, 95 (5-6) : 656 - 669
[6] The orthoprojection widths of some classes of periodic functions of two variables with a given majorant of the mixed moduli of continuity
Pustovoitov, NN
[J]. IZVESTIYA MATHEMATICS, 2000, 64 (01) : 121 - 141
[7] ESTIMATES FOR THE APPROXIMATE CHARACTERISTICS OF THE CLASSES Bp,θΩ OF PERIODIC FUNCTIONS OF TWO VARIABLES WITH GIVEN MAJORANT OF MIXED MODULI OF CONTINUITY
Konohrai, A. F.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2011, 63 (02) : 209 - 221
[8] On the Kolmogorov widths of classes of functions with given mixed moduli of continuity
Pustovoitov, N. N.
[J]. ANALYSIS MATHEMATICA, 2012, 38 (01) : 41 - 64
[9] О поперечниках no Колмогорову классов функций с заданным смешанным модулем непрерывностиOn the Kolmogorov widths of classes of functions with given mixed moduli of continuity
Н. Н. Пустовойтов
[J]. Analysis Mathematica, 2012, 38 (1) : 41 - 64
[10] ESTIMATES OF APPROXIMATIVE CHARACTERISTICS OF THE CLASSES Bp,θΩ OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES WITH GIVEN MAJORANT OF MIXED MODULI OF CONTINUITY IN THE SPACE Lq
Fedunyk-Yaremchuk, O., V
Hembars'ka, S. B.
[J]. CARPATHIAN MATHEMATICAL PUBLICATIONS, 2019, 11 (02) : 281 - 295

← 1 2 3 4 5 →