{"title":"关于一般Haar系统中傅立叶级数的发散性","authors":"M. Grigoryan, A. Maranjyan","doi":"10.52737/18291163-2021.13.6-1-10","DOIUrl":null,"url":null,"abstract":"For any countable set $D \\subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]\\backslash D$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the divergence of Fourier series in the general Haar system\",\"authors\":\"M. Grigoryan, A. Maranjyan\",\"doi\":\"10.52737/18291163-2021.13.6-1-10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any countable set $D \\\\subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]\\\\backslash D$.\",\"PeriodicalId\":42323,\"journal\":{\"name\":\"Armenian Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Armenian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52737/18291163-2021.13.6-1-10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2021.13.6-1-10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the divergence of Fourier series in the general Haar system
For any countable set $D \subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]\backslash D$.
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