The inverse theorem in various metrics of approximation theory for periodic functions with monotone Fourier coefficients

被引：1

作者：

Il'yasov, N. A. ^{[1
]}

机构：

[1] Baku State Univ, Sci Phys Math, Baku, Azerbaijan

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2016年 / 22卷 / 04期

关键词：

modulus of smoothness; best approximation; inverse theorem in various metrics; trigonometric Fourier series with monotone coefficients; order-sharp inequality on a class;

D O I：

10.21538/0134-4889-2016-22-4-153-162

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the exactness with respect to order of an upper bound for the kth-order modulus of smoothness in L-q(T) in terms of the elements of a sequence of best approximations in L-p(T) on the class of all functions with monotonically decreasing Fourier coefficients, where 1 < p < q < infinity and k is an element of N.

引用

页码：153 / 162

页数：10

共 14 条

[1] The Direct Theorem of the Theory of Approximation of Periodic Functions with Monotone Fourier Coefficients in Different Metrics
Il'yasov, N. A.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2018, 303 : 100 - 114
[2] The Direct Theorem of the Theory of Approximation of Periodic Functions with Monotone Fourier Coefficients in Different Metrics
N. A. Il’yasov
Proceedings of the Steklov Institute of Mathematics, 2018, 303 : 100 - 114
[3] ON THE CONVERSE THEOREM OF APPROXIMATION IN VARIOUS METRICS FOR NONPERIODIC FUNCTIONS
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[7] Inverse Theorems on the Approximation of Periodic Functions with High Generalized Smoothness
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[8] Direct and Inverse Theorems in Approximation Theory for Periodic Functions in SB Stechkin's Papers and the Development of These Theorems
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PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2011, 273 : S1 - S13
[9] Direct and inverse theorems in approximation theory for periodic functions in S.B. Stechkin’s papers and the development of these theorems
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Proceedings of the Steklov Institute of Mathematics, 2011, 273 : 1 - 13
[10] Direct and inverse theorems in approximation theory for periodic functions in S.B. Stechkin's papers and the development of these theorems
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TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2010, 16 (04): : 5 - 17

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