{"title":"绝对收敛的傅里叶-雅可比级数和广义Lipschitz类","authors":"Faouaz Saadi, R. Daher","doi":"10.1080/10652469.2022.2122460","DOIUrl":null,"url":null,"abstract":"In this paper, we give necessary and sufficient conditions in terms of Fourier–Jacobi coefficients of a function f, to ensure that f belongs either to one of the generalized Lipschitz classes and for and . Also a condition for generalized Jacobi differentiability of a function on interval is proved.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"334 - 345"},"PeriodicalIF":0.7000,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes\",\"authors\":\"Faouaz Saadi, R. Daher\",\"doi\":\"10.1080/10652469.2022.2122460\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give necessary and sufficient conditions in terms of Fourier–Jacobi coefficients of a function f, to ensure that f belongs either to one of the generalized Lipschitz classes and for and . Also a condition for generalized Jacobi differentiability of a function on interval is proved.\",\"PeriodicalId\":54972,\"journal\":{\"name\":\"Integral Transforms and Special Functions\",\"volume\":\"34 1\",\"pages\":\"334 - 345\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-09-19\",\"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/10.1080/10652469.2022.2122460\",\"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/10.1080/10652469.2022.2122460","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes
In this paper, we give necessary and sufficient conditions in terms of Fourier–Jacobi coefficients of a function f, to ensure that f belongs either to one of the generalized Lipschitz classes and for and . Also a condition for generalized Jacobi differentiability of a function on interval is proved.
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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.
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