{"title":"一般最优多项式逼近、稳定和统一的投影","authors":"Christopher Felder","doi":"10.4208/ata.OA-2020-0047","DOIUrl":null,"url":null,"abstract":"For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"General Optimal Polynomial Approximants, Stabilization, and Projections of Unity\",\"authors\":\"Christopher Felder\",\"doi\":\"10.4208/ata.OA-2020-0047\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.\",\"PeriodicalId\":29763,\"journal\":{\"name\":\"Analysis in Theory and Applications\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis in Theory and Applications\",\"FirstCategoryId\":\"95\",\"ListUrlMain\":\"https://doi.org/10.4208/ata.OA-2020-0047\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis in Theory and Applications","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.4208/ata.OA-2020-0047","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
General Optimal Polynomial Approximants, Stabilization, and Projections of Unity
For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.