{"title":"康托尔集合上的傅立叶变换和展开图","authors":"Tuomas Sahlsten, Connor Stevens","doi":"10.1353/ajm.2024.a932433","DOIUrl":null,"url":null,"abstract":"<p><p>abstract:</p><p>We study the Fourier transforms $\\widehat{\\mu}(\\xi)$ of non-atomic Gibbs measures $\\mu$ for uniformly expanding maps $T$ of bounded distortions on $[0,1]$ or Cantor sets with strong separation. When $T$ is totally non-linear, then $\\widehat{\\mu}(\\xi)\\to 0$ at a polynomial rate as $|\\xi|\\to\\infty$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fourier transform and expanding maps on Cantor sets\",\"authors\":\"Tuomas Sahlsten, Connor Stevens\",\"doi\":\"10.1353/ajm.2024.a932433\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>abstract:</p><p>We study the Fourier transforms $\\\\widehat{\\\\mu}(\\\\xi)$ of non-atomic Gibbs measures $\\\\mu$ for uniformly expanding maps $T$ of bounded distortions on $[0,1]$ or Cantor sets with strong separation. When $T$ is totally non-linear, then $\\\\widehat{\\\\mu}(\\\\xi)\\\\to 0$ at a polynomial rate as $|\\\\xi|\\\\to\\\\infty$.</p></p>\",\"PeriodicalId\":7453,\"journal\":{\"name\":\"American Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1353/ajm.2024.a932433\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2024.a932433","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Fourier transform and expanding maps on Cantor sets
abstract:
We study the Fourier transforms $\widehat{\mu}(\xi)$ of non-atomic Gibbs measures $\mu$ for uniformly expanding maps $T$ of bounded distortions on $[0,1]$ or Cantor sets with strong separation. When $T$ is totally non-linear, then $\widehat{\mu}(\xi)\to 0$ at a polynomial rate as $|\xi|\to\infty$.
期刊介绍：
The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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