Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums

被引：0

作者：

Semenova, T. Yu. ^{[1
,2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119991, Russia

[2] Moscow Ctr Fundamental & Appl Math, Moscow 119991, Russia

来源：

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 30卷 / 04期

关键词：

D O I：

10.1134/S1061920823040179

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered. DOI 10.1134/S1061920823040179

引用

页码：691 / 700

页数：10

共 50 条

[1] Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums
T.Yu. Semenova
[J]. Russian Journal of Mathematical Physics, 2023, 30 : 691 - 700
[2] On approximation of periodic functions by Fourier sums
Zhuk V.V.
[J]. Journal of Mathematical Sciences, 2010, 166 (2) : 167 - 185
[3] APPROXIMATION OF CONTINUOUS PERIODIC-FUNCTIONS OF MANY VARIABLES BY THE FOURIER SUMS
GAVRILYUK, VT
[J]. DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1981, (02): : 8 - 10
[4] Approximation of Continuous 2π-Periodic Piecewise Smooth Functions by Discrete Fourier Sums
Akniyev, G. G.
[J]. IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2019, 19 (01): : 4 - 15
[5] SIMULTANEOUS APPROXIMATION OF PERIODIC FUNCTIONS AND THEIR DERIVATIVES BY FOURIER SUMS
STEPANETS, AI
[J]. DOKLADY AKADEMII NAUK SSSR, 1980, 254 (03): : 543 - 544
[6] Approximation of Poisson integrals of continuous functions by Fourier sums
Stepanets, AI
[J]. DOKLADY MATHEMATICS, 2000, 62 (01) : 41 - 43
[7] On the approximation of continuous functions by Fourier-Legendre sums
Bashmakova, I
Rafalson, S
[J]. JOURNAL OF APPROXIMATION THEORY, 1996, 86 (02) : 197 - 215
[8] APPROXIMATION OF CERTAIN CLASSES OF CONTINUOUS FUNCTIONS BY FOURIER SUMS AND FEJER SUMS
EFIMOV, AV
[J]. DOKLADY AKADEMII NAUK SSSR, 1957, 114 (05): : 930 - 933
[9] FOURIER SUM APPROXIMATION OF CONTINUOUS PERIODIC FUNCTIONS
GAVRILIUK, VT
STECHKIN, SB
[J]. DOKLADY AKADEMII NAUK SSSR, 1978, 241 (03): : 525 - 527
[10] CLASSES OF PERIODIC-FUNCTIONS AND THE APPROXIMATION OF THEIR ELEMENTS BY FOURIER SUMS
STEPANETS, AI
[J]. DOKLADY AKADEMII NAUK SSSR, 1984, 277 (05): : 1074 - 1077

← 1 2 3 4 5 →