{"title":"On uniform convergence of infinite products","authors":"K. M. Slepenchuk, G. A. Barbashova","doi":"10.15421/247720","DOIUrl":null,"url":null,"abstract":"We establish necessary and sufficient conditions for $\\{ \\alpha_k(x) \\}$ to satisfy such that the product $\\prod\\limits_{k=1}^{\\infty} [1+\\alpha_k(x) U_k(x)]$ converges uniformly under the condition that $\\{ U_k(x) \\}$ belongs to a given class.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"58 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Researches in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/247720","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We establish necessary and sufficient conditions for $\{ \alpha_k(x) \}$ to satisfy such that the product $\prod\limits_{k=1}^{\infty} [1+\alpha_k(x) U_k(x)]$ converges uniformly under the condition that $\{ U_k(x) \}$ belongs to a given class.