{"title":"傅立叶框架的非谱分形测度","authors":"Chun-Kit Lai, Yang Wang","doi":"10.4171/JFG/52","DOIUrl":null,"url":null,"abstract":"We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal exponentials (and hence it does not admit any exponential orthonormal bases), but it still admits Fourier frames.","PeriodicalId":48484,"journal":{"name":"Journal of Fractal Geometry","volume":"4 1","pages":"305-327"},"PeriodicalIF":1.1000,"publicationDate":"2015-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/52","citationCount":"18","resultStr":"{\"title\":\"Non-spectral fractal measures with Fourier frames\",\"authors\":\"Chun-Kit Lai, Yang Wang\",\"doi\":\"10.4171/JFG/52\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal exponentials (and hence it does not admit any exponential orthonormal bases), but it still admits Fourier frames.\",\"PeriodicalId\":48484,\"journal\":{\"name\":\"Journal of Fractal Geometry\",\"volume\":\"4 1\",\"pages\":\"305-327\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2015-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/JFG/52\",\"citationCount\":\"18\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fractal Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/JFG/52\",\"RegionNum\":4,\"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":"Journal of Fractal Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/JFG/52","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal exponentials (and hence it does not admit any exponential orthonormal bases), but it still admits Fourier frames.
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