c ^1 -范数的调和近似

Mathematics of The Ussr-sbornik Pub Date : 1992-02-28 DOI:10.1070/SM1992V071N01ABEH002129

P. V. Paramonov

{"title":"c ^1 -范数的调和近似","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":"{\"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}","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

摘要

的紧子集上的-范数中的调和函数，特别是调和多项式，建立了调和函数逼近的可能性的判据。这个准则，是用调和容量表示的，与维图什金关于解析容量的有理逼近的定理是一个自然的类比。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

ON HARMONIC APPROXIMATION IN THE $ C^1$-NORM

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematics of The Ussr-sbornik

自引率

0.00%

发文量

期刊最新文献

ON A PROPERTY OF THE SUBDIFFERENTIAL ON THE TRACE FORMULAS OF GEL'FAND-LEVITAN AND KREĬN ASYMPTOTICS OF THE COEFFICIENT OF QUASICONFORMALITY, AND THE BOUNDARY BEHAVIOR OF A MAPPING OF A BALL ON FUNCTIONS WITH SIMILAR VALUES FOR MINIMAL DEVIATIONS FROM POLYNOMIALS AND RATIONAL FUNCTIONS THE SPACE BMO AND STRONG MEANS OF FOURIER-WALSH SERIES