{"title":"On the Classification of Points of a Unit Circle for Subharmonic Functions of the Class $$\\mathfrak{A}{\\kern 1pt} \\text{*}$$","authors":"S. L. Berberyan","doi":"10.3103/s1066369x24700117","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A class <span>\\(\\mathfrak{A}{\\kern 1pt} \\text{*}\\)</span> consisting of subharmonic functions in the unit disk such that their superpositions with some families of linear fractional automorphisms of the disk form normal families is considered. A theorem stating that for any function of class <span>\\(\\mathfrak{A}{\\kern 1pt} \\text{*}\\)</span> the set of points of the unit circle can be represented as a union of a set of Fatou points, a set of generalized Plesner points, and a set of measure zero is proved.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"49 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700117","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A class \(\mathfrak{A}{\kern 1pt} \text{*}\) consisting of subharmonic functions in the unit disk such that their superpositions with some families of linear fractional automorphisms of the disk form normal families is considered. A theorem stating that for any function of class \(\mathfrak{A}{\kern 1pt} \text{*}\) the set of points of the unit circle can be represented as a union of a set of Fatou points, a set of generalized Plesner points, and a set of measure zero is proved.
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