On the boundedness of general partial sums

IF 0.6 3区 数学 Q3 MATHEMATICS
Vakhtang Tsagareishvili
{"title":"On the boundedness of general partial sums","authors":"Vakhtang Tsagareishvili","doi":"10.1007/s10998-023-00565-y","DOIUrl":null,"url":null,"abstract":"<p>From S. Banach’s results it follows that even for the function <span>\\(f(x)=1\\)</span> <span>\\((x\\in [0,1])\\)</span> the general partial sums of its general Fourier series are not bounded a.e. on [0, 1]. In the present paper, we find conditions for the functions <span>\\(\\varphi _n\\)</span> of an orthonormal system <span>\\((\\varphi _n\\)</span>) under which the partial sums of functions from some differentiable class are bounded. We prove that the obtained results are best possible. We also investigate the properties of subsequences of general orthonormal systems.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"30 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Periodica Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-023-00565-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

From S. Banach’s results it follows that even for the function \(f(x)=1\) \((x\in [0,1])\) the general partial sums of its general Fourier series are not bounded a.e. on [0, 1]. In the present paper, we find conditions for the functions \(\varphi _n\) of an orthonormal system \((\varphi _n\)) under which the partial sums of functions from some differentiable class are bounded. We prove that the obtained results are best possible. We also investigate the properties of subsequences of general orthonormal systems.

论一般偏和的有界性
从 S. Banach 的结果可以看出,即使是函数 \(f(x)=1\)\((x\in[0,1]))的一般傅里叶级数的一般部分和在[0,1]上也不是有界的。在本文中,我们为正交系统 \((\varphi _n\))的函数 \((\varphi _n\))找到了条件,在这些条件下,来自某个可微分类的函数的偏和是有界的。我们证明所得到的结果是最好的。我们还研究了一般正交系统子序列的性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.40
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信