L2和相关空间的Gabor框架

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2021-01-01 DOI:10.1201/9781003210450-4

J. Benedetto, D. Walnut

{"title":"L2和相关空间的Gabor框架","authors":"J. Benedetto, D. Walnut","doi":"10.1201/9781003210450-4","DOIUrl":null,"url":null,"abstract":"The basic theory of frames is reviewed, and special topics dealing with Gabor frames and decompositions are developed. These topics include Gabor decompositions of L1 and of Bessel potential spaces. (Sobolev spaces are Bessel potential spaces.) Frames of translates in L2 are characterized; and the Balian–Low theorem for L2 is proved. The former result is not only useful for the Gabor theory, but is the basis of multiresolution analysis frames; the latter result is related to the classical uncertainty principle inequality.","PeriodicalId":50282,"journal":{"name":"International Journal of Wavelets Multiresolution and Information Processing","volume":"271 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Gabor frames for L2 and related spaces\",\"authors\":\"J. Benedetto, D. Walnut\",\"doi\":\"10.1201/9781003210450-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The basic theory of frames is reviewed, and special topics dealing with Gabor frames and decompositions are developed. These topics include Gabor decompositions of L1 and of Bessel potential spaces. (Sobolev spaces are Bessel potential spaces.) Frames of translates in L2 are characterized; and the Balian–Low theorem for L2 is proved. The former result is not only useful for the Gabor theory, but is the basis of multiresolution analysis frames; the latter result is related to the classical uncertainty principle inequality.\",\"PeriodicalId\":50282,\"journal\":{\"name\":\"International Journal of Wavelets Multiresolution and Information Processing\",\"volume\":\"271 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Wavelets Multiresolution and Information Processing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1201/9781003210450-4\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Wavelets Multiresolution and Information Processing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1201/9781003210450-4","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}

引用次数: 14

摘要

回顾了框架的基本理论，并对Gabor框架及其分解进行了专题讨论。这些主题包括L1和贝塞尔势空间的Gabor分解。(索博列夫空间是贝塞尔势空间。)第二语言翻译的框架具有特征;并证明了L2的Balian-Low定理。前者的结果不仅对Gabor理论有用，而且是多分辨率分析框架的基础;后一个结果与经典测不准原理不等式有关。

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

Gabor frames for L2 and related spaces

The basic theory of frames is reviewed, and special topics dealing with Gabor frames and decompositions are developed. These topics include Gabor decompositions of L1 and of Bessel potential spaces. (Sobolev spaces are Bessel potential spaces.) Frames of translates in L2 are characterized; and the Balian–Low theorem for L2 is proved. The former result is not only useful for the Gabor theory, but is the basis of multiresolution analysis frames; the latter result is related to the classical uncertainty principle inequality.

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

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.