{"title":"抽象希尔伯特空间中的一致采样近似法","authors":"Sinuk Kang, Kil Hyun Kwon, Dae Gwan Lee","doi":"10.3390/axioms13070489","DOIUrl":null,"url":null,"abstract":"This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"60 16","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Consistent Sampling Approximations in Abstract Hilbert Spaces\",\"authors\":\"Sinuk Kang, Kil Hyun Kwon, Dae Gwan Lee\",\"doi\":\"10.3390/axioms13070489\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.\",\"PeriodicalId\":502355,\"journal\":{\"name\":\"Axioms\",\"volume\":\"60 16\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Axioms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/axioms13070489\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Axioms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/axioms13070489","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Consistent Sampling Approximations in Abstract Hilbert Spaces
This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.
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