The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space Lq

被引：0

作者：

Shvai K.V. ^{[1
]}

机构：

[1] Institute of Mathematics of the NAS of Ukraine, Kiev

来源：

Journal of Mathematical Sciences | 2017年 / 222卷 / 6期

关键词：

Bernoulli kernel; de la Vallée–Poissin kernel; Fourier series; stepwise hyperbolic cross; The best trigonometric approximation;

D O I：

10.1007/s10958-017-3329-0

中图分类号：

学科分类号：

摘要：

The order estimates of the best M-term trigonometric approximations of functions Dβψ and the classes of (ψ , β)-differentiable periodic multivariate functions in the space Lq, 2 ≤ q < ∞ are obtained. It is shown that, under certain conditions imposed on the parameter q; the best M-term trigonometric approximations eM(Lβ,1ψ)q have better order than the best orthogonal trigonometric approximations e1M(Lβ,1ψ)q. © 2017, Springer Science+Business Media New York.

引用

页码：750 / 761

页数：11

共 50 条

[21] ON BEST M-TERM APPROXIMATIONS AND THE ENTROPY OF SETS IN THE SPACE L(1)
KASHIN, BS
TEMLYAKOV, VN
MATHEMATICAL NOTES, 1994, 56 (5-6) : 1137 - 1157
[22] On Connection of m-Term and Best Approximations of Some Classes of Sequences in the Spaces lp
N. L. Kudryavtsev
Moscow University Mathematics Bulletin, 2020, 75 : 27 - 33
[23] Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric
Romanyuk, A. S.
MATHEMATICAL NOTES, 2007, 82 (1-2) : 216 - 228
[24] On the best M-term approximations of functions from the Nikol'skii-Besov class in the Lorentz space
Akishev, Gabdolla
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2022, 28 (01): : 7 - 26
[25] Best orthogonal trigonometric approximations of the classes BΩp,θ of periodic functions of many variables
S. P. Voitenko
Ukrainian Mathematical Journal, 2009, 61 : 1728 - 1742
[26] Best trigonometric approximations for some classes of periodic functions of several variables in the uniform metric
A. S. Romanyuk
Mathematical Notes, 2007, 82 : 216 - 228
[27] On estimates of the order of the best M-term approximations of functions of several variables in the anisotropic Lorentz-Zygmund space
Akishev, G.
IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS, 2023, 23 (02): : 142 - 156
[28] Best Orthogonal Trigonometric Approximations of the Nikol’skii–Besov-Type Classes of Periodic Functions in the Space B∞,1
S. B. Hembars’ka
P. V. Zaderei
Ukrainian Mathematical Journal, 2022, 74 : 883 - 895
[29] Best Orthogonal Trigonometric Approximations of the Nikol'skii-Besov-Type Classes of Periodic Functions in the Space B∞,1
Hembars'ka, S. B.
Zaderei, P., V
UKRAINIAN MATHEMATICAL JOURNAL, 2022, 74 (06) : 883 - 895
[30] Best approximations and kolmogorov and trigonometric widths of the classes B p,θ Ω of periodic functions of many variables
Stasyuk S.A.
Ukrainian Mathematical Journal, 2004, 56 (11) : 1849 - 1863

← 1 2 3 4 5 →