{"title":"具有广义多分辨率结构的子空间仿射伪帧及金字塔分解格式","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":"{\"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}","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}
Subspace Affine Pseudoframes with a Generalized Multiresolution Structure and the Pyramid Decomposition Scheme
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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