On the nonclassical approximation method for periodic functions by trigonometric polynomials

被引：3

作者：

Kolomoitsev Y.S. ^{[1
]}

Trigub R.M. ^{[2
]}

机构：

[1] Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, 74, R. Luxemburg Str., Donetsk

[2] Donetsk National University, 24, Universitetskaya Str., Donetsk

来源：

Journal of Mathematical Sciences | 2013年 / 188卷 / 2期

关键词：

Fourier series; Fourier transformation of a measure; K-functional; moduli of smoothness; multiplier; principle of comparison of multipliers; Wiener's 1/f theorem;

D O I：

10.1007/s10958-012-1111-x

中图分类号：

学科分类号：

摘要：

We study the approximation of functions by linear polynomial means of their Fourier series with a function-multiplier φ that is equal to 1 not only at zero, in contrast with classical methods of summability. The exact order of convergence to zero of the sequence, (f̂k are Fourier coefficients) as n → ∞ is obtained. The answer is given in terms of the values of difference operators of a continuous function f and a special K-functional (step of π/n). In addition, we obtain not only the sufficient conditions for φ but the necessary ones as well. © 2012 Springer Science+Business Media New York.

引用

页码：113 / 127

页数：14

共 50 条

[21] APPROXIMATION AND SATURATION OF PERIODIC CONTINUOUS-FUNCTIONS BY CERTAIN TRIGONOMETRIC INTERPOLATION POLYNOMIALS
SUNOUCHI, G
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1976, 27 (3-4): : 323 - 328
[22] CONCERNING ORDER OF APPROXIMATION OF PERIODIC CONTINUOUS-FUNCTIONS BY TRIGONOMETRIC INTERPOLATION POLYNOMIALS
VARMA, AK
ISRAEL JOURNAL OF MATHEMATICS, 1972, 12 (04) : 337 - &
[23] Multiplicator type operators and approximation of periodic functions of one variable by trigonometric polynomials
Runovskii, K. V.
SBORNIK MATHEMATICS, 2021, 212 (02) : 234 - 264
[24] APPROXIMATION OF A CERTAIN CLASS OF PERIODIC FUNCTIONS OF MANY VARIABLES USING TRIGONOMETRIC POLYNOMIALS
BABENKO, KI
DOKLADY AKADEMII NAUK SSSR, 1960, 132 (05): : 982 - 985
[25] Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials in integral metric
Serdyuk A.S.
Ukrainian Mathematical Journal, 2001, 53 (12) : 2014 - 2026
[26] Approximation of periodic analytic functions by interpolation trigonometric polynomials in the metric of the space L
Serdyuk A.S.
Ukrainian Mathematical Journal, 2002, 54 (5) : 852 - 861
[27] METHOD FOR APPROXIMATION OF CONTINUOUS PERIODIC FUNCTIONS BY TRIGONOMETRICAL POLYNOMIALS
KIS, O
CAO, HT
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1976, 28 (3-4): : 367 - 381
[28] LOCAL PROPERTIES OF FUNCTIONS AND APPROXIMATION BY TRIGONOMETRIC POLYNOMIALS
RADOSLAVOVA, TV
MATHEMATICAL NOTES, 1975, 18 (3-4) : 903 - 910
[29] Approximation of Ω—bandlimited Functions by Ω—bandlimited Trigonometric Polynomials
R. Martin
Sampling Theory in Signal and Image Processing, 2007, 6 (3): : 273 - 296
[30] MONOTONE-APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
SHADRIN, AY
MATHEMATICAL NOTES, 1983, 34 (3-4) : 669 - 675

← 1 2 3 4 5 →