{"title":"TWISTED SHIFT-INVARIANT SYSTEM IN \n$L^2(\\mathbb {R}^{2N})$","authors":"Santi Ranjan Das, R. Velsamy, Radha Ramakrishnan","doi":"10.1017/nmj.2023.11","DOIUrl":null,"url":null,"abstract":"Abstract We consider a general twisted shift-invariant system, \n$V^{t}(\\mathcal {A})$\n , consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system \n$V^{t}(\\mathcal {A})$\n to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2023.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We consider a general twisted shift-invariant system,
$V^{t}(\mathcal {A})$
, consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system
$V^{t}(\mathcal {A})$
to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.
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