{"title":"用矩阵法求$r$倍微分傅里叶级数和$r$倍微分共轭傅里叶级数在$p \\geqslant 1$次上的绝对和强求和性","authors":"N. Polovina","doi":"10.15421/247719","DOIUrl":null,"url":null,"abstract":"We establish conditions of $|\\gamma|_p$- and $[\\gamma]_p$-summability in degree $p \\geqslant 1$ of $r$ times differentiated Fourier series at the point where $\\gamma = \\| \\gamma_{nk} \\|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"63 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Absolute and strong summability in degree $p \\\\geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods\",\"authors\":\"N. Polovina\",\"doi\":\"10.15421/247719\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish conditions of $|\\\\gamma|_p$- and $[\\\\gamma]_p$-summability in degree $p \\\\geqslant 1$ of $r$ times differentiated Fourier series at the point where $\\\\gamma = \\\\| \\\\gamma_{nk} \\\\|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.\",\"PeriodicalId\":52827,\"journal\":{\"name\":\"Researches in Mathematics\",\"volume\":\"63 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/10.15421/247719\",\"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/10.15421/247719","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods
We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.