离散Jacobi–Sobolev空间中傅立叶级数的收敛性

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2023-03-07 DOI:10.1080/10652469.2023.2182777

Ó. Ciaurri, J. Mínguez Ceniceros, J. Rodríguez

{"title":"离散Jacobi–Sobolev空间中傅立叶级数的收敛性","authors":"Ó. Ciaurri, J. Mínguez Ceniceros, J. Rodríguez","doi":"10.1080/10652469.2023.2182777","DOIUrl":null,"url":null,"abstract":"In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"703 - 720"},"PeriodicalIF":0.7000,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On convergence of Fourier series in discrete Jacobi–Sobolev spaces\",\"authors\":\"Ó. Ciaurri, J. Mínguez Ceniceros, J. Rodríguez\",\"doi\":\"10.1080/10652469.2023.2182777\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem.\",\"PeriodicalId\":54972,\"journal\":{\"name\":\"Integral Transforms and Special Functions\",\"volume\":\"34 1\",\"pages\":\"703 - 720\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Integral Transforms and Special Functions\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/10652469.2023.2182777\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Transforms and Special Functions","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10652469.2023.2182777","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文给出了离散Sobolev空间中具有Jacobi测度的部分和算子的一致有界性的一个完整刻画。结果，我们得到了傅立叶级数的收敛性。此外，还证明了这个Sobolev空间是第一类，这意味着不可能应用Banach–Steinhaus定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On convergence of Fourier series in discrete Jacobi–Sobolev spaces

In this paper, we show a complete characterization of the uniform boundedness of the partial sum operator in a discrete Sobolev space with Jacobi measure. As a consequence, we obtain the convergence of the Fourier series. Moreover it is showed that this Sobolev space is the first category which implies that it is not possible to apply the Banach–Steinhaus theorem.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Integral Transforms and Special Functions 数学-数学

CiteScore

2.20

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.