{"title":"$$L^2[0,1]$$ l2上Hardy算子的Beurling定理[0]","authors":"Jim Agler, John E. McCarthy","doi":"10.1007/s44146-023-00073-y","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that the invariant subspaces of the Hardy operator on <span>\\(L^2[0,1]\\)</span> are the spaces that are limits of sequences of finite dimensional spaces spanned by monomial functions.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"573 - 592"},"PeriodicalIF":0.5000,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Beurling’s theorem for the Hardy operator on \\\\(L^2[0,1]\\\\)\",\"authors\":\"Jim Agler, John E. McCarthy\",\"doi\":\"10.1007/s44146-023-00073-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove that the invariant subspaces of the Hardy operator on <span>\\\\(L^2[0,1]\\\\)</span> are the spaces that are limits of sequences of finite dimensional spaces spanned by monomial functions.</p></div>\",\"PeriodicalId\":46939,\"journal\":{\"name\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"volume\":\"89 3-4\",\"pages\":\"573 - 592\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACTA SCIENTIARUM MATHEMATICARUM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s44146-023-00073-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-023-00073-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Beurling’s theorem for the Hardy operator on \(L^2[0,1]\)
We prove that the invariant subspaces of the Hardy operator on \(L^2[0,1]\) are the spaces that are limits of sequences of finite dimensional spaces spanned by monomial functions.
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