{"title":"用傅里叶和估计连续周期函数的近似值","authors":"T.Yu. Semenova","doi":"10.1134/S1061920823040179","DOIUrl":null,"url":null,"abstract":"<p> An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered. </p><p> <b> DOI</b> 10.1134/S1061920823040179 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"691 - 700"},"PeriodicalIF":1.7000,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums\",\"authors\":\"T.Yu. Semenova\",\"doi\":\"10.1134/S1061920823040179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered. </p><p> <b> DOI</b> 10.1134/S1061920823040179 </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"30 4\",\"pages\":\"691 - 700\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920823040179\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823040179","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
摘要 根据函数的连续性模数，得到了函数与其傅里叶级数部分和之差的近似精确估计值。考虑了小于最佳值的参数连续性模数值。 doi 10.1134/s1061920823040179
Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums
An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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