{"title":"Uniform Rational Approximation of Even and Odd Continuations of Functions","authors":"T. S. Mardvilko","doi":"10.1134/s0001434624010206","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The behavior of the best rational approximations of an odd continuation of a function is studied. It is shown that without additional conditions on the smoothness of the function, it is impossible to estimate the best rational approximation of the odd continuation of the function on <span>\\([-1,1]\\)</span> in terms of the best rational approximation of the original function on <span>\\([0,1]\\)</span>. A sharp upper bound is found for the best rational approximations of an even (odd) continuation of a function in terms of an odd (even) continuation and an extremal Blaschke product. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624010206","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The behavior of the best rational approximations of an odd continuation of a function is studied. It is shown that without additional conditions on the smoothness of the function, it is impossible to estimate the best rational approximation of the odd continuation of the function on \([-1,1]\) in terms of the best rational approximation of the original function on \([0,1]\). A sharp upper bound is found for the best rational approximations of an even (odd) continuation of a function in terms of an odd (even) continuation and an extremal Blaschke product.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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