{"title":"作为覆盖图的 $$*$$ - 指数","authors":"Amedeo Altavilla, Samuele Mongodi","doi":"10.1007/s40315-024-00558-z","DOIUrl":null,"url":null,"abstract":"<p>We employ tools from complex analysis to construct the <span>\\(*\\)</span>-logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the <span>\\(*\\)</span>-exponential; we establish sufficient conditions for the <span>\\(*\\)</span>-product of two <span>\\(*\\)</span>-exponentials to also be a <span>\\(*\\)</span>-exponential; we calculate the slice derivative of the <span>\\(*\\)</span>-exponential of a regular function.\n</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"23 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The $$*$$ -Exponential as a Covering Map\",\"authors\":\"Amedeo Altavilla, Samuele Mongodi\",\"doi\":\"10.1007/s40315-024-00558-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We employ tools from complex analysis to construct the <span>\\\\(*\\\\)</span>-logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the <span>\\\\(*\\\\)</span>-exponential; we establish sufficient conditions for the <span>\\\\(*\\\\)</span>-product of two <span>\\\\(*\\\\)</span>-exponentials to also be a <span>\\\\(*\\\\)</span>-exponential; we calculate the slice derivative of the <span>\\\\(*\\\\)</span>-exponential of a regular function.\\n</p>\",\"PeriodicalId\":49088,\"journal\":{\"name\":\"Computational Methods and Function Theory\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods and Function Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40315-024-00558-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods and Function Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00558-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We employ tools from complex analysis to construct the \(*\)-logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the \(*\)-exponential; we establish sufficient conditions for the \(*\)-product of two \(*\)-exponentials to also be a \(*\)-exponential; we calculate the slice derivative of the \(*\)-exponential of a regular function.
期刊介绍：
CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
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