{"title":"The Nehari-Schwarz lemma and infinitesimal boundary rigidity of bounded holomorphic functions","authors":"Oliver Roth","doi":"10.24193/subbmath.2022.2.05","DOIUrl":null,"url":null,"abstract":"\"We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self{maps of the unit disk. In particular, we discuss the case of in nitely many critical points and its relation to the zero sets and invariant subspaces for Bergman spaces, as well as the case of equality at the boundary.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"40 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Universitatis BabesBolyai Geologia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/subbmath.2022.2.05","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
"We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self{maps of the unit disk. In particular, we discuss the case of in nitely many critical points and its relation to the zero sets and invariant subspaces for Bergman spaces, as well as the case of equality at the boundary."
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