{"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":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"251 1","pages":"734 - 767"},"PeriodicalIF":0.8000,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nagoya Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2023.11","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.
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