{"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}
引用次数: 0
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.
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