分数单调系数正弦级数和的渐近性

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica 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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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.