Approximation of classes of periodic functions in several variables

被引：6

作者：

Romanyuk, AS ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Math Inst, UA-252143 Kiev, Ukraine

来源：

MATHEMATICAL NOTES | 2002年 / 71卷 / 1-2期

关键词：

orthogonal trigonometric approximation; Besov class of functions; multiple Fourier sum; staircase hyperbolic Fourier sum; Rudin-Shapiro polynomials;

D O I：

10.1023/A:1013982425195

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We stud the approximation of the classes B-p(r),(theta) and W-p(r),(alpha) of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums.

引用

页码：98 / 109

页数：12

共 50 条

[1] Approximation of Classes of Periodic Functions in Several Variables
A. S. Romanyuk
Mathematical Notes, 2002, 71 : 98 - 109
[2] Best approximation of periodic functions of several variables from the classes
Stasyuk, S. A.
UKRAINIAN MATHEMATICAL JOURNAL, 2012, 64 (01) : 156 - 161
[3] Approximation of classes Bpr,θ of periodic functions of one and several variables
Romanyuk, A. S.
MATHEMATICAL NOTES, 2010, 87 (3-4) : 403 - 415
[4] Approximation of classes Bp, θ Ω of periodic functions in several variables by linear methods
Konograi, A. F.
ANALYSIS MATHEMATICA, 2013, 39 (03) : 217 - 233
[5] Diameters and best approximation of the classes Bpr of periodic functions of several variables
Romanyuk, A. S.
ANALYSIS MATHEMATICA, 2011, 37 (03) : 181 - 213
[6] APPROXIMATION OF CLASSES OF PERIODIC-FUNCTIONS OF SEVERAL VARIABLES BY NUCLEAR OPERATORS
GALEEV, EM
MATHEMATICAL NOTES, 1990, 47 (3-4) : 248 - 254
[7] Приближение классов Bp, θΩ, периодических функций многих переменных линейными методамиApproximation of classes Bp, θΩ of periodic functions in several variables by linear methods
А. Ф. Конограй
Analysis Mathematica, 2013, 39 : 217 - 233
[8] Wavelet approximation and Fourier widths of classes of periodic functions of several variables. II
Bazarkhanov, D. B.
ANALYSIS MATHEMATICA, 2012, 38 (04) : 249 - 289
[9] BEST LINEAR METHODS FOR APPROXIMATION OF CLASSES OF PERIODIC-FUNCTIONS OF SEVERAL-VARIABLES
ZUNG, D
MATHEMATICAL NOTES, 1987, 41 (5-6) : 361 - 365
[10] 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.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2021, 13 (03) : 838 - 850

← 1 2 3 4 5 →