{"title":"可近似数上支持的度量的傅立叶衰减锐估计值","authors":"Robert Fraser, Thanh Nguyen","doi":"arxiv-2409.02854","DOIUrl":null,"url":null,"abstract":"We construct a measure on the well-approximable numbers whose Fourier\ntransform decays at a nearly optimal rate. This gives a logarithmic improvement\non a previous construction of Kaufman.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sharp Fourier decay estimates for measures supported on the well-approximable numbers\",\"authors\":\"Robert Fraser, Thanh Nguyen\",\"doi\":\"arxiv-2409.02854\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct a measure on the well-approximable numbers whose Fourier\\ntransform decays at a nearly optimal rate. This gives a logarithmic improvement\\non a previous construction of Kaufman.\",\"PeriodicalId\":501145,\"journal\":{\"name\":\"arXiv - MATH - Classical Analysis and ODEs\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Classical Analysis and ODEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.02854\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02854","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sharp Fourier decay estimates for measures supported on the well-approximable numbers
We construct a measure on the well-approximable numbers whose Fourier
transform decays at a nearly optimal rate. This gives a logarithmic improvement
on a previous construction of Kaufman.
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