{"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":0.7000,"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}
引用次数: 18
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.
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