{"title":"关于无穷积的一致收敛","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":"{\"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}","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}
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.
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