{"title":"ON HARMONIC APPROXIMATION IN THE $ C^1$-NORM","authors":"P. V. Paramonov","doi":"10.1070/SM1992V071N01ABEH002129","DOIUrl":null,"url":null,"abstract":"A criterion is established for the possibility of approximation by harmonic functions and, in particular, by harmonic polynomials in the -norm on compact subsets of . This criterion, which is in terms of harmonic -capacity in , yields a natural analog to the theorem of Vitushkin on rational approximation in terms of analytic capacity.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"71 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"52","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N01ABEH002129","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 52
Abstract
A criterion is established for the possibility of approximation by harmonic functions and, in particular, by harmonic polynomials in the -norm on compact subsets of . This criterion, which is in terms of harmonic -capacity in , yields a natural analog to the theorem of Vitushkin on rational approximation in terms of analytic capacity.
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