{"title":"Balayage是一个射线系统和整个功能的完全规则生长","authors":"B. Khabibullin","doi":"10.1070/IM1992V038N01ABEH002192","DOIUrl":null,"url":null,"abstract":"This paper presents a technique for constructing functions that are subharmonic in the complex plane, agree with a given subharmonic function u on a system S of rays with vertex at the origin, and are harmonic outside S. For a wide class of systems S, this technique permits one to obtain criteria for the complete regularity of growth of entire functions f on S in terms of the balayage of the distribution of zeros of f.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"BALAYAGE ON A SYSTEM OF RAYS AND ENTIRE FUNCTIONS OF COMPLETELY REGULAR GROWTH\",\"authors\":\"B. Khabibullin\",\"doi\":\"10.1070/IM1992V038N01ABEH002192\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a technique for constructing functions that are subharmonic in the complex plane, agree with a given subharmonic function u on a system S of rays with vertex at the origin, and are harmonic outside S. For a wide class of systems S, this technique permits one to obtain criteria for the complete regularity of growth of entire functions f on S in terms of the balayage of the distribution of zeros of f.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1992V038N01ABEH002192\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1992V038N01ABEH002192","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
BALAYAGE ON A SYSTEM OF RAYS AND ENTIRE FUNCTIONS OF COMPLETELY REGULAR GROWTH
This paper presents a technique for constructing functions that are subharmonic in the complex plane, agree with a given subharmonic function u on a system S of rays with vertex at the origin, and are harmonic outside S. For a wide class of systems S, this technique permits one to obtain criteria for the complete regularity of growth of entire functions f on S in terms of the balayage of the distribution of zeros of f.
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