{"title":"半平面上有限阶解析函数空间内插问题","authors":"K. Malyutin, Alexander L. Gusev","doi":"10.15393/J3.ART.2018.5170","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order ρ > 1 in the half-plane. The necessary and sufficient conditions for its solvability in terms of the canonical Nevanlinna product of nodes of interpolation are obtained. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"75 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The interpolation problem in the spaces of analytical functions of finite order in the half-plane\",\"authors\":\"K. Malyutin, Alexander L. Gusev\",\"doi\":\"10.15393/J3.ART.2018.5170\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order ρ > 1 in the half-plane. The necessary and sufficient conditions for its solvability in terms of the canonical Nevanlinna product of nodes of interpolation are obtained. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series.\",\"PeriodicalId\":41813,\"journal\":{\"name\":\"Problemy Analiza-Issues of Analysis\",\"volume\":\"75 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Problemy Analiza-Issues of Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15393/J3.ART.2018.5170\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Problemy Analiza-Issues of Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15393/J3.ART.2018.5170","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The interpolation problem in the spaces of analytical functions of finite order in the half-plane
The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order ρ > 1 in the half-plane. The necessary and sufficient conditions for its solvability in terms of the canonical Nevanlinna product of nodes of interpolation are obtained. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series.
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