{"title":"Convergence of two-point Padé approximants to piecewise holomorphic functions","authors":"M. Yattselev","doi":"10.1070/SM9024","DOIUrl":null,"url":null,"abstract":"Let and be formal power series at the origin and infinity, and , , be the rational function that simultaneously interpolates at the origin with order and at infinity with order . When germs and represent multi-valued functions with finitely many branch points, it was shown by Buslaev that there exists a unique compact set in the complement of which the approximants converge in capacity to the approximated functions. The set may or may not separate the plane. We study uniform convergence of the approximants for the geometrically simplest sets that do separate the plane. Bibliography: 26 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"45 1","pages":"1626 - 1659"},"PeriodicalIF":0.8000,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9024","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Let and be formal power series at the origin and infinity, and , , be the rational function that simultaneously interpolates at the origin with order and at infinity with order . When germs and represent multi-valued functions with finitely many branch points, it was shown by Buslaev that there exists a unique compact set in the complement of which the approximants converge in capacity to the approximated functions. The set may or may not separate the plane. We study uniform convergence of the approximants for the geometrically simplest sets that do separate the plane. Bibliography: 26 titles.
期刊介绍:
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in:
Mathematical analysis
Ordinary differential equations
Partial differential equations
Mathematical physics
Geometry
Algebra
Functional analysis