{"title":"Restricted T-Universal Functions","authors":"W. Luh, V. A. Martirosian, J. Müller","doi":"10.1006/jath.2001.3640","DOIUrl":null,"url":null,"abstract":"We prove the existence of a function @f which is holomorphic exactly in the unit disk D and has universal translates with respect to a prescribed closed set [email protected][email protected]?D and satisfies @[email protected]?C^~(@?D\\E). If Q is a subsequence of N\"0 with upper density d(Q)=1 then the function @f can be constructed such that in [email protected] (z)[email protected]?n=0~a\"nz^nwitha\"[email protected]?Q.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"107 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Approx. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1006/jath.2001.3640","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
We prove the existence of a function @f which is holomorphic exactly in the unit disk D and has universal translates with respect to a prescribed closed set [email protected][email protected]?D and satisfies @[email protected]?C^~(@?D\E). If Q is a subsequence of N"0 with upper density d(Q)=1 then the function @f can be constructed such that in [email protected] (z)[email protected]?n=0~a"nz^nwitha"[email protected]?Q.
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