{"title":"论正交序列的收敛性和可求和性","authors":"L. Gogoladze","doi":"10.3103/s1068362324700171","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the paper, the sufficient conditions are found for the convergence, summability by the Cesàro methods and unconditional convergence almost everywhere of orthogonal series, which are equivalent to the well-known theorems of Menshov–Redemacher, Menshov, and Orlich.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"54 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Convergence and Summability of Orthogonal Series\",\"authors\":\"L. Gogoladze\",\"doi\":\"10.3103/s1068362324700171\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In the paper, the sufficient conditions are found for the convergence, summability by the Cesàro methods and unconditional convergence almost everywhere of orthogonal series, which are equivalent to the well-known theorems of Menshov–Redemacher, Menshov, and Orlich.</p>\",\"PeriodicalId\":54854,\"journal\":{\"name\":\"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences\",\"volume\":\"54 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2024-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3103/s1068362324700171\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700171","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Convergence and Summability of Orthogonal Series
Abstract
In the paper, the sufficient conditions are found for the convergence, summability by the Cesàro methods and unconditional convergence almost everywhere of orthogonal series, which are equivalent to the well-known theorems of Menshov–Redemacher, Menshov, and Orlich.
期刊介绍：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.
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