{"title":"两个或两个以上实变量的分量次加性函数的Fekete引理","authors":"Silvio Capobianco","doi":"10.12697/acutm.2022.26.04","DOIUrl":null,"url":null,"abstract":"We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a similar result for functions of integer variables. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments expand on those in Chapter 6 of E. Hille's 1948 textbook.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":"85 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Fekete's lemma for componentwise subadditive functions of two or more real variables\",\"authors\":\"Silvio Capobianco\",\"doi\":\"10.12697/acutm.2022.26.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a similar result for functions of integer variables. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments expand on those in Chapter 6 of E. Hille's 1948 textbook.\",\"PeriodicalId\":42426,\"journal\":{\"name\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"volume\":\"85 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta et Commentationes Universitatis Tartuensis de Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12697/acutm.2022.26.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta et Commentationes Universitatis Tartuensis de Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12697/acutm.2022.26.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Fekete's lemma for componentwise subadditive functions of two or more real variables
We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a similar result for functions of integer variables. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments expand on those in Chapter 6 of E. Hille's 1948 textbook.
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