{"title":"A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators","authors":"A. Perälä, J. Virtanen, L. Wolf","doi":"10.2478/conop-2012-0004","DOIUrl":null,"url":null,"abstract":"Abstract We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2013-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2478/conop-2012-0004","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/conop-2012-0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
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