{"title":"多重富兰克林级数的唯一性定理","authors":"K. Navasardyan","doi":"10.46991/pysu:a/2017.51.3.241","DOIUrl":null,"url":null,"abstract":"It is proved, that if the square partial sums $\\sigma_{q_n}(\\textbf{x})$ of a multiple Franklin series converge in measure to a function $f$, the ratio $\\dfrac{q_{n+1}}{q_n}$ is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function $f$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"57 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"UNIQUENESS THEOREMS FOR MULTIPLE FRANKLIN SERIES\",\"authors\":\"K. Navasardyan\",\"doi\":\"10.46991/pysu:a/2017.51.3.241\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is proved, that if the square partial sums $\\\\sigma_{q_n}(\\\\textbf{x})$ of a multiple Franklin series converge in measure to a function $f$, the ratio $\\\\dfrac{q_{n+1}}{q_n}$ is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function $f$.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"57 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2017.51.3.241\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2017.51.3.241","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is proved, that if the square partial sums $\sigma_{q_n}(\textbf{x})$ of a multiple Franklin series converge in measure to a function $f$, the ratio $\dfrac{q_{n+1}}{q_n}$ is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function $f$.
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