{"title":"论几乎周期函数傅里叶级数的绝对收敛性","authors":"Yu. Kh. Khasanov, F. M. Talbakov","doi":"10.3103/s1066369x24700282","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper investigates sufficient conditions for the absolute convergence of trigonometric Fourier series of almost-periodic functions in the sense of Besikovitch in the case when the Fourier exponents have a single limiting point at infinity. A higher-order modulus of continuity is used as a structural characteristic of the function under consideration.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"199 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Absolute Convergence of Fourier Series of Almost Periodic Functions\",\"authors\":\"Yu. Kh. Khasanov, F. M. Talbakov\",\"doi\":\"10.3103/s1066369x24700282\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>The paper investigates sufficient conditions for the absolute convergence of trigonometric Fourier series of almost-periodic functions in the sense of Besikovitch in the case when the Fourier exponents have a single limiting point at infinity. A higher-order modulus of continuity is used as a structural characteristic of the function under consideration.</p>\",\"PeriodicalId\":46110,\"journal\":{\"name\":\"Russian Mathematics\",\"volume\":\"199 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3103/s1066369x24700282\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700282","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Absolute Convergence of Fourier Series of Almost Periodic Functions
Abstract
The paper investigates sufficient conditions for the absolute convergence of trigonometric Fourier series of almost-periodic functions in the sense of Besikovitch in the case when the Fourier exponents have a single limiting point at infinity. A higher-order modulus of continuity is used as a structural characteristic of the function under consideration.
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