复变量函数的h全纯性和h解析性

BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series Pub Date : 1900-01-01 DOI:10.32523/2616-7182/2020-133-4-19-27

V. Pavlovsky, I. L. Vasiliev

{"title":"复变量函数的h全纯性和h解析性","authors":"V. Pavlovsky, I. L. Vasiliev","doi":"10.32523/2616-7182/2020-133-4-19-27","DOIUrl":null,"url":null,"abstract":"Interest in the study of the properties of functions defined on the set of \\textit{h}-complex numbers arose again in connection with existing applications in geometry and mechanics. In this paper, we present necessary and sufficient conditions for \\textit{h}-differentiability and \\textit{h}-holomorphy of functions of an \\textit{h}-complex variable, the theorem on finite increments is proved, sufficient conditions for \\textit{h}-analyticity are found, a uniqueness theorem for \\textit{h}-analytic functions is proved.","PeriodicalId":225533,"journal":{"name":"BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series","volume":"100 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON h-HOLOMORPHY AND h-ANALYTICITY OF FUNCTIONS OF AN h-COMPLEX VARIABLE\",\"authors\":\"V. Pavlovsky, I. L. Vasiliev\",\"doi\":\"10.32523/2616-7182/2020-133-4-19-27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Interest in the study of the properties of functions defined on the set of \\\\textit{h}-complex numbers arose again in connection with existing applications in geometry and mechanics. In this paper, we present necessary and sufficient conditions for \\\\textit{h}-differentiability and \\\\textit{h}-holomorphy of functions of an \\\\textit{h}-complex variable, the theorem on finite increments is proved, sufficient conditions for \\\\textit{h}-analyticity are found, a uniqueness theorem for \\\\textit{h}-analytic functions is proved.\",\"PeriodicalId\":225533,\"journal\":{\"name\":\"BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series\",\"volume\":\"100 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32523/2616-7182/2020-133-4-19-27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32523/2616-7182/2020-133-4-19-27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

对于研究在\textit{h} -复数集合上定义的函数的性质的兴趣，由于在几何学和力学中的现有应用而再次出现。本文给出了\textit{h} -复变量函数的\textit{h} -可微性和\textit{h} -全纯性的充分必要条件，证明了有限增量定理，得到了\textit{h} -可解析性的充分条件，证明了\textit{h} -解析函数的唯一性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

ON h-HOLOMORPHY AND h-ANALYTICITY OF FUNCTIONS OF AN h-COMPLEX VARIABLE

Interest in the study of the properties of functions defined on the set of \textit{h}-complex numbers arose again in connection with existing applications in geometry and mechanics. In this paper, we present necessary and sufficient conditions for \textit{h}-differentiability and \textit{h}-holomorphy of functions of an \textit{h}-complex variable, the theorem on finite increments is proved, sufficient conditions for \textit{h}-analyticity are found, a uniqueness theorem for \textit{h}-analytic functions is proved.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

BULLETIN of L.N. Gumilyov Eurasian National University. MATHEMATICS. COMPUTER SCIENCE. MECHANICS Series

自引率

0.00%

发文量