Approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2(0,∞)

被引：0

作者：

V. V. Arestov

M. A. Filatova

机构：

[1] Ural Federal University,Institute of Mathematics and Computer Science

[2] Ural Branch of the Russian Academy of Sciences,Institute of Mathematics and Mechanics

来源：

Proceedings of the Steklov Institute of Mathematics | 2014年 / 284卷

关键词：

Stechkin’s problem; differentiation operator; semiaxis;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We give an upper estimate for the value of the best approximation of the (firstorder) differentiation operator by linear bounded operators on the class of twice differentiable functions in the space L2(0,∞). This upper estimate is close to a known lower estimate and improves previously known upper estimates. To prove the upper estimate, we consider a specific family of operators; in this family, we choose an operator that provides the least estimate for the value of the best approximation.

引用

页码：24 / 40

页数：16

共 50 条

[41] Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(). I
Vakarchuk, S. B.
UKRAINIAN MATHEMATICAL JOURNAL, 2019, 70 (09) : 1345 - 1374
[42] NUMERICAL APPROXIMATION OF NON-LINEAR FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH L2 INITIAL FUNCTIONS
REDDIEN, GW
WEBB, GF
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1978, 9 (06) : 1151 - 1171
[43] Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(ℝ). I
S. B. Vakarchuk
Ukrainian Mathematical Journal, 2019, 70 : 1345 - 1374
[44] On n-K Width of Certain Function Classes Defined by Linear Operators in L2 Space
YU Rui-fang
WU Ga-ridi
Chinese Quarterly Journal of Mathematics, 2016, (01) : 96 - 101
[45] Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(ℝ). II
S. B. Vakarchuk
Ukrainian Mathematical Journal, 2019, 70 : 1550 - 1584
[46] A linear backward Euler scheme for a class of degenerate advection- diffusion equations: A mathematical analysis of the convergence in L∞(0, T0; L2(Ω)) and in L2(0, T0; H1(Ω))
Fadimba, Koffi B.
ANALYSIS AND APPLICATIONS, 2014, 12 (03) : 227 - 249
[47] On Conditions of the Completeness of Some Systems of Bessel Functions in the Space L2((0; 1); x2pdx)
Khats, R., V
AZERBAIJAN JOURNAL OF MATHEMATICS, 2021, 11 (01): : 3 - 10
[48] Approximation in the Mean for the Classes Of Functions in the Space L2[(0,1); x] by The Fourier-Bessel Sums And Estimation of the Values of Their n-Widths
Vakarchuk, Sergii
Vakarchuk, Mykhailo
UKRAINIAN MATHEMATICAL JOURNAL, 2024, 76 (02) : 214 - 242
[49] Upper Bounds for the Approximation of Some Classes of Bivariate Functions by Triangular Fourier-Hermite Sums in the Space L2,ρ(ℝ2)
M. Sh. Shabozov
O. A. Dzhurakhonov
Analysis Mathematica, 2019, 45 : 823 - 840
[50] Some questions on approximation of functions of several variables by Fourier sums in the space L2((a,b)n;p(x))
Abilov, MV
Aigunov, GA
RUSSIAN MATHEMATICAL SURVEYS, 2004, 59 (06) : 1205 - 1206

← 1 2 3 4 5 →