$L^2（\mathbb｛R｝^｛2N｝）中的扭转平移不变系统$

IF 0.8 2区数学 Q2 MATHEMATICS

Nagoya Mathematical Journal Pub Date : 2023-06-05 DOI:10.1017/nmj.2023.11

Santi Ranjan Das, R. Velsamy, Radha Ramakrishnan

{"title":"$L^2（\\mathbb｛R｝^｛2N｝）中的扭转平移不变系统$","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":"{\"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}","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

摘要

摘要我们考虑了一个由可数多个生成元的扭曲平移组成的一般扭曲移位不变系统$V^｛t｝（\mathcal｛a｝）$，并研究了获得系统$V^{t｝的特征以形成帧序列或Riesz序列的问题。我们用一些例子来说明我们的理论。除这些结果外，我们还研究了一个双扭移不变量系统，并从给定的扭平移序列Riesz中得到了一个扭平移的正交序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

TWISTED SHIFT-INVARIANT SYSTEM IN $L^2(\mathbb {R}^{2N})$

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

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.