片状考奇-黎曼算子的积分公式及其应用

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-06-24 DOI:10.1007/s00006-024-01338-7
Chao Ding, Xiaoqian Cheng
{"title":"片状考奇-黎曼算子的积分公式及其应用","authors":"Chao Ding,&nbsp;Xiaoqian Cheng","doi":"10.1007/s00006-024-01338-7","DOIUrl":null,"url":null,"abstract":"<div><p>The theory of slice regular functions has been developed rapidly in the past few years, and most properties are given in slices at the early stage. In 2013, Colombo et al. introduced a non-constant coefficients differential operator to describe slice regular functions globally, and this brought the study of slice regular functions in a global sense. In this article, we introduce a slice Cauchy–Riemann operator, which is motivated by the non-constant coefficients differential operator mentioned above. Then, A Borel–Pompeiu formula for this slice Cauchy–Riemann operator is discovered, which leads to a Cauchy integral formula for slice regular functions. A Plemelj integral formula for the slice Cauchy–Riemann operator is introduced, which gives rise to results on slice regular extension at the end.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integral Formulas for Slice Cauchy–Riemann Operator and Applications\",\"authors\":\"Chao Ding,&nbsp;Xiaoqian Cheng\",\"doi\":\"10.1007/s00006-024-01338-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The theory of slice regular functions has been developed rapidly in the past few years, and most properties are given in slices at the early stage. In 2013, Colombo et al. introduced a non-constant coefficients differential operator to describe slice regular functions globally, and this brought the study of slice regular functions in a global sense. In this article, we introduce a slice Cauchy–Riemann operator, which is motivated by the non-constant coefficients differential operator mentioned above. Then, A Borel–Pompeiu formula for this slice Cauchy–Riemann operator is discovered, which leads to a Cauchy integral formula for slice regular functions. A Plemelj integral formula for the slice Cauchy–Riemann operator is introduced, which gives rise to results on slice regular extension at the end.</p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00006-024-01338-7\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-024-01338-7","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

切片正则函数理论在过去几年得到了快速发展,早期大部分性质都是在切片中给出的。2013 年,Colombo 等人引入了一个非常数系数微分算子来全局描述切片正则函数,这带来了全局意义上的切片正则函数研究。在本文中,我们引入了一个切片 Cauchy-Riemann 算子,它是由上述非常数系数微分算子激发的。然后,我们发现了该片 Cauchy-Riemann 算子的 Borel-Pompeiu 公式,并由此得到了片正则函数的 Cauchy 积分公式。最后,引入了切片 Cauchy-Riemann 算子的 Plemelj 积分公式,从而得出切片正则扩展的结果。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Integral Formulas for Slice Cauchy–Riemann Operator and Applications

The theory of slice regular functions has been developed rapidly in the past few years, and most properties are given in slices at the early stage. In 2013, Colombo et al. introduced a non-constant coefficients differential operator to describe slice regular functions globally, and this brought the study of slice regular functions in a global sense. In this article, we introduce a slice Cauchy–Riemann operator, which is motivated by the non-constant coefficients differential operator mentioned above. Then, A Borel–Pompeiu formula for this slice Cauchy–Riemann operator is discovered, which leads to a Cauchy integral formula for slice regular functions. A Plemelj integral formula for the slice Cauchy–Riemann operator is introduced, which gives rise to results on slice regular extension at the end.

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
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
期刊最新文献
Management of Cholesteatoma: Hearing Rehabilitation. Congenital Cholesteatoma. Evaluation of Cholesteatoma. Management of Cholesteatoma: Extension Beyond Middle Ear/Mastoid. Recidivism and Recurrence.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1