{"title":"整个函数和联合变量中l指标的有界性","authors":"Andriy Ivanovych Bandura","doi":"10.46793/kgjmat2204.595b","DOIUrl":null,"url":null,"abstract":"In the paper, we present sufficient conditions of boundedness of L-index in joint variables for a sum of entire functions, where L : C n → R n + is a continuous function, R+ = (0, +∞). They are applicable to a very wide class of entire functions because for every entire function F in C n with bounded multiplicities of zero points there exists a positive continuous function L such that F has bounded L-index in joint variables. Our propositions are generalizations of Pugh’s result obtained for entire functions of one variable of bounded index.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"BOUNDEDNESS OF L-INDEX IN JOINT VARIABLES FOR SUM OF ENTIRE FUNCTIONS\",\"authors\":\"Andriy Ivanovych Bandura\",\"doi\":\"10.46793/kgjmat2204.595b\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the paper, we present sufficient conditions of boundedness of L-index in joint variables for a sum of entire functions, where L : C n → R n + is a continuous function, R+ = (0, +∞). They are applicable to a very wide class of entire functions because for every entire function F in C n with bounded multiplicities of zero points there exists a positive continuous function L such that F has bounded L-index in joint variables. Our propositions are generalizations of Pugh’s result obtained for entire functions of one variable of bounded index.\",\"PeriodicalId\":44902,\"journal\":{\"name\":\"Kragujevac Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kragujevac Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46793/kgjmat2204.595b\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kragujevac Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46793/kgjmat2204.595b","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
摘要
本文给出了一类完整函数和在联合变量上L指标有界的充分条件，其中L: C n→R n +是连续函数，R+ =(0， +∞)。它们适用于非常广泛的整函数类因为对于C n中的每一个整函数F具有0点的有界多重度存在一个正的连续函数L使得F在联合变量中有界的L指标。我们的命题推广了Pugh关于单变量有界指标全函数的结论。
BOUNDEDNESS OF L-INDEX IN JOINT VARIABLES FOR SUM OF ENTIRE FUNCTIONS
In the paper, we present sufficient conditions of boundedness of L-index in joint variables for a sum of entire functions, where L : C n → R n + is a continuous function, R+ = (0, +∞). They are applicable to a very wide class of entire functions because for every entire function F in C n with bounded multiplicities of zero points there exists a positive continuous function L such that F has bounded L-index in joint variables. Our propositions are generalizations of Pugh’s result obtained for entire functions of one variable of bounded index.
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