{"title":"单位圆盘上一类亚纯函数的Wiman-Valiron理论","authors":"J. Langley, J. Rossi","doi":"10.3318/PRIA.2014.114.14","DOIUrl":null,"url":null,"abstract":"Analogues of the key results of Wiman-Valiron theory are proved for a class of functions meromorphic in the unit disc, based on an approach developed by Bergweiler, Rippon and Stallard for the plane setting. The results give local approximations for the function and its logarithmic derivative and, in the case of positive order of growth, for higher order logarithmic derivatives as well.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wiman-Valiron theory for a class of functions meromorphic in the unit disc\",\"authors\":\"J. Langley, J. Rossi\",\"doi\":\"10.3318/PRIA.2014.114.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Analogues of the key results of Wiman-Valiron theory are proved for a class of functions meromorphic in the unit disc, based on an approach developed by Bergweiler, Rippon and Stallard for the plane setting. The results give local approximations for the function and its logarithmic derivative and, in the case of positive order of growth, for higher order logarithmic derivatives as well.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2014.114.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2014.114.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Wiman-Valiron theory for a class of functions meromorphic in the unit disc
Analogues of the key results of Wiman-Valiron theory are proved for a class of functions meromorphic in the unit disc, based on an approach developed by Bergweiler, Rippon and Stallard for the plane setting. The results give local approximations for the function and its logarithmic derivative and, in the case of positive order of growth, for higher order logarithmic derivatives as well.
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