{"title":"Subspace Affine Pseudoframes with a Generalized Multiresolution Structure and the Pyramid Decomposition Scheme","authors":"Xiaofeng Wang, Fengling Zhang","doi":"10.1109/ICIME.2010.5477499","DOIUrl":null,"url":null,"abstract":"The rise of frame theory in applied mathe-unities is due to the flexibility and redundancy of frames. In this work, the notion of a generalized multiresolution structure of L2(R) is proposed. The definition of multiple pseudoframes for subspaces of L2(R) is given. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is derived based on such a generalized multiresolution structure. The pyramid decomposition scheme is also obtained.","PeriodicalId":135441,"journal":{"name":"2009 International Conference on Computational Intelligence and Software Engineering","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Computational Intelligence and Software Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICIME.2010.5477499","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
The rise of frame theory in applied mathe-unities is due to the flexibility and redundancy of frames. In this work, the notion of a generalized multiresolution structure of L2(R) is proposed. The definition of multiple pseudoframes for subspaces of L2(R) is given. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of L2(R) is investigated. The sufficient condition for the existence of multiple pseudoframes for subspaces of L2(R) is derived based on such a generalized multiresolution structure. The pyramid decomposition scheme is also obtained.
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