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

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