{"title":"关于具有里兹均值的傅里叶级数的 $$L^1$$ 收敛性的说明","authors":"H. S. Özarslan, M. Ö. Şakar","doi":"10.1134/s000143462403009x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, the problem of <span>\\(L^1\\)</span>-convergence of Fourier series with quasi-monotone coefficients is handled by using the <span>\\((\\bar{N},p_n)\\)</span>-mean. Also, an example is given about the Fourier series of a signal (function) <span>\\(f\\)</span> and its <span>\\((\\bar{N},p_n)\\)</span> mean. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"13 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on $$L^1$$ -Convergence of Fourier Series with Riesz Mean\",\"authors\":\"H. S. Özarslan, M. Ö. Şakar\",\"doi\":\"10.1134/s000143462403009x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> In this paper, the problem of <span>\\\\(L^1\\\\)</span>-convergence of Fourier series with quasi-monotone coefficients is handled by using the <span>\\\\((\\\\bar{N},p_n)\\\\)</span>-mean. Also, an example is given about the Fourier series of a signal (function) <span>\\\\(f\\\\)</span> and its <span>\\\\((\\\\bar{N},p_n)\\\\)</span> mean. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s000143462403009x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s000143462403009x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Note on $$L^1$$ -Convergence of Fourier Series with Riesz Mean
Abstract
In this paper, the problem of \(L^1\)-convergence of Fourier series with quasi-monotone coefficients is handled by using the \((\bar{N},p_n)\)-mean. Also, an example is given about the Fourier series of a signal (function) \(f\) and its \((\bar{N},p_n)\) mean.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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