一个超复变正则性的统一概念

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-05-06 DOI:10.1016/j.geomphys.2024.105219

Riccardo Ghiloni , Caterina Stoppato

{"title":"一个超复变正则性的统一概念","authors":"Riccardo Ghiloni , Caterina Stoppato","doi":"10.1016/j.geomphys.2024.105219","DOIUrl":null,"url":null,"abstract":"<div><p>We define a very general notion of regularity for functions taking values in an alternative real ⁎-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternions, in addition to subsuming the notions of Fueter-regular function and of slice-regular function, it gives rise to an entirely new theory, which we develop in some detail.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0393044024001207/pdfft?md5=8d470d5ac0915c71c54a27a10f9b1919&pid=1-s2.0-S0393044024001207-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A unified notion of regularity in one hypercomplex variable\",\"authors\":\"Riccardo Ghiloni , Caterina Stoppato\",\"doi\":\"10.1016/j.geomphys.2024.105219\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We define a very general notion of regularity for functions taking values in an alternative real ⁎-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternions, in addition to subsuming the notions of Fueter-regular function and of slice-regular function, it gives rise to an entirely new theory, which we develop in some detail.</p></div>\",\"PeriodicalId\":55602,\"journal\":{\"name\":\"Journal of Geometry and Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0393044024001207/pdfft?md5=8d470d5ac0915c71c54a27a10f9b1919&pid=1-s2.0-S0393044024001207-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Geometry and Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0393044024001207\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometry and Physics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0393044024001207","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们为在另一个实⁎-代数中取值的函数定义了一个非常一般的正则性概念。在克利福德数上，这个概念包含了已经确立的单元函数和片元函数的概念。在四元数上，除了包含傅特不规则函数和片不规则函数的概念之外，它还产生了一种全新的理论，我们将对其进行详细阐述。

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

A unified notion of regularity in one hypercomplex variable

We define a very general notion of regularity for functions taking values in an alternative real ⁎-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternions, in addition to subsuming the notions of Fueter-regular function and of slice-regular function, it gives rise to an entirely new theory, which we develop in some detail.

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

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity