{"title":"ON FUNCTIONS WITH SIMILAR VALUES FOR MINIMAL DEVIATIONS FROM POLYNOMIALS AND RATIONAL FUNCTIONS","authors":"Kh. M. Makhmudov","doi":"10.1070/SM1993V074N02ABEH003353","DOIUrl":null,"url":null,"abstract":"The author establishes that, for every function that is analytic inside the unit disk and belongs to the space with 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>, the equation is satisfied, where and are the minimal deviations of from polynomials of degree at most and from rational functions of order at most . In particular, if and only if can be continued analytically over the disk .There is also a similar proposition for the approximation of functions in the spaces , 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1993V074N02ABEH003353","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
The author establishes that, for every function that is analytic inside the unit disk and belongs to the space with 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>, the equation is satisfied, where and are the minimal deviations of from polynomials of degree at most and from rational functions of order at most . In particular, if and only if can be continued analytically over the disk .There is also a similar proposition for the approximation of functions in the spaces , 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>.
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