分数单调系数正弦级数和的渐近性

Pub Date : 2023-01-23 DOI:10.1007/s10476-023-0186-6

M. I. Dyachenko, A. P. Solodov

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引用次数: 1

摘要

我们研究了以下问题：根据函数\（v\left（｛\boldsymbol｛b｝｝，x｝\right）=\sum\lolimits_｛k=1｝^\infty｛b_k｝）=x\sum\limits_{k=1｝^｛\pi/x｝\ right]｝｛k｝\），哪个单调性阶意味着正弦级数的和的上下估计。我们的研究结果在定性水平上完成了由R.Salem开始并由S.Izumi、S.a.Telyakovskiĭ和a.Yu继续的研究。波波夫。

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Asymptotics of Sums of Sine Series with Fractional Monotonicity Coefficients

We study the following question: which monotonicity order implies upper and lower estimates of the sum of a sine series \(g\left( {{\boldsymbol{b}},x} \right) = \sum\nolimits_{k = 1}^\infty {{b_k}} \) sin kx near zero in terms of the function \(v\left( {{\boldsymbol{b}},x} \right) = x\sum\nolimits_{k = 1}^{\left[ {\pi /x} \right]} {k{b_k}} \). Our results complete, on a qualitative level, the studies began by R. Salem and continued by S. Izumi, S. A. Telyakovskiĭ and A. Yu. Popov.

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