{"title":"Overcompleteness of coherent frames for unimodular amenable groups","authors":"","doi":"10.4310/arkiv.2023.v61.n2.a2","DOIUrl":null,"url":null,"abstract":". This paper concerns the overcompleteness of coherent frames for amenable unimodular groups. It is shown that for coherent frames associated with an integrable vector a set of positive Beurling density can be removed yet still leave a frame. The obtained results extend various theorems of [J. Fourier Anal. Appl., 12(3):307-344, 2006] to frames with non-Abelian index sets.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arkiv for Matematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/arkiv.2023.v61.n2.a2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
. This paper concerns the overcompleteness of coherent frames for amenable unimodular groups. It is shown that for coherent frames associated with an integrable vector a set of positive Beurling density can be removed yet still leave a frame. The obtained results extend various theorems of [J. Fourier Anal. Appl., 12(3):307-344, 2006] to frames with non-Abelian index sets.
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