{"title":"右型群上的切向k-Cauchy-Fueter算子及其Bochner-Martinelli型公式","authors":"Yun Shi, Guangzhen Ren","doi":"10.1007/s00006-023-01267-x","DOIUrl":null,"url":null,"abstract":"<div><p>The <i>k</i>-Cauchy–Fueter operator and the tangential <i>k</i>-Cauchy–Fueter operator are the quaternionic counterpart of Cauchy–Riemann operator and the tangential Cauchy–Riemann operator in the theory of several complex variables, respectively. In Wang (On the boundary complex of the <i>k</i>-Cauchy–Fueter complex, arXiv:2210.13656), Wang introduced the notion of right-type groups, which have the structure of nilpotent Lie groups of step-two, and many aspects of quaternionic analysis can be generalized to this kind of group. In this paper we generalize the right-type group to any step-two case, and introduce the generalization of Cauchy–Fueter operator on <span>\\({\\mathbb {H}}^n\\times {\\mathbb {R}}^r.\\)</span> Then we establish the Bochner–Martinelli type formula for tangential <i>k</i>-Cauchy–Fueter operator on stratified right-type groups.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 2","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula\",\"authors\":\"Yun Shi, Guangzhen Ren\",\"doi\":\"10.1007/s00006-023-01267-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The <i>k</i>-Cauchy–Fueter operator and the tangential <i>k</i>-Cauchy–Fueter operator are the quaternionic counterpart of Cauchy–Riemann operator and the tangential Cauchy–Riemann operator in the theory of several complex variables, respectively. In Wang (On the boundary complex of the <i>k</i>-Cauchy–Fueter complex, arXiv:2210.13656), Wang introduced the notion of right-type groups, which have the structure of nilpotent Lie groups of step-two, and many aspects of quaternionic analysis can be generalized to this kind of group. In this paper we generalize the right-type group to any step-two case, and introduce the generalization of Cauchy–Fueter operator on <span>\\\\({\\\\mathbb {H}}^n\\\\times {\\\\mathbb {R}}^r.\\\\)</span> Then we establish the Bochner–Martinelli type formula for tangential <i>k</i>-Cauchy–Fueter operator on stratified right-type groups.</p></div>\",\"PeriodicalId\":7330,\"journal\":{\"name\":\"Advances in Applied Clifford Algebras\",\"volume\":\"33 2\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Clifford Algebras\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00006-023-01267-x\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01267-x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula
The k-Cauchy–Fueter operator and the tangential k-Cauchy–Fueter operator are the quaternionic counterpart of Cauchy–Riemann operator and the tangential Cauchy–Riemann operator in the theory of several complex variables, respectively. In Wang (On the boundary complex of the k-Cauchy–Fueter complex, arXiv:2210.13656), Wang introduced the notion of right-type groups, which have the structure of nilpotent Lie groups of step-two, and many aspects of quaternionic analysis can be generalized to this kind of group. In this paper we generalize the right-type group to any step-two case, and introduce the generalization of Cauchy–Fueter operator on \({\mathbb {H}}^n\times {\mathbb {R}}^r.\) Then we establish the Bochner–Martinelli type formula for tangential k-Cauchy–Fueter operator on stratified right-type groups.
期刊介绍:
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.