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.
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页码：113 / 127
页数：14
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