{"title":"Partial Gabor frames and dual frames","authors":"Yu Tian, Hui-Fang Jia, Guo-Liang He","doi":"10.1142/S0219691321500351","DOIUrl":null,"url":null,"abstract":"The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.","PeriodicalId":158567,"journal":{"name":"Int. J. Wavelets Multiresolution Inf. Process.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Wavelets Multiresolution Inf. Process.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0219691321500351","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.
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