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...
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| Veröffentlicht in: | Advances in applied Clifford algebras 2023-04, Vol.33 (2), Article 22 |
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| creator | Shi, Yun Ren, Guangzhen |
| description | 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
H
n
×
R
r
.
Then we establish the Bochner–Martinelli type formula for tangential
k
-Cauchy–Fueter operator on stratified right-type groups. |
| doi_str_mv | 10.1007/s00006-023-01267-x |
| format | Article |
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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
H
n
×
R
r
.
Then we establish the Bochner–Martinelli type formula for tangential
k
-Cauchy–Fueter operator on stratified right-type groups.</description><identifier>ISSN: 0188-7009</identifier><identifier>EISSN: 1661-4909</identifier><identifier>DOI: 10.1007/s00006-023-01267-x</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Complex variables ; Lie groups ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Physics ; Physics and Astronomy ; Theoretical</subject><ispartof>Advances in applied Clifford algebras, 2023-04, Vol.33 (2), Article 22</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-7cfa363b8aabb8409d9b89465a36b1f5ab28ac8ca3a10c8d702d25e46b208af43</cites><orcidid>0000-0002-4197-0367</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00006-023-01267-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00006-023-01267-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Shi, Yun</creatorcontrib><creatorcontrib>Ren, Guangzhen</creatorcontrib><title>The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula</title><title>Advances in applied Clifford algebras</title><addtitle>Adv. Appl. Clifford Algebras</addtitle><description>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
H
n
×
R
r
.
Then we establish the Bochner–Martinelli type formula for tangential
k
-Cauchy–Fueter operator on stratified right-type groups.</description><subject>Applications of Mathematics</subject><subject>Complex variables</subject><subject>Lie groups</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Theoretical</subject><issn>0188-7009</issn><issn>1661-4909</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kM9Kw0AQhxdRsFZfwNOC59XZ3fzZHLXYWqgUpJ6XSbppUtMk7ibQ3nwH39AncW0Eb85lYPh-v4GPkGsOtxwgvnPgJ2IgJAMuopjtT8iIRxFnQQLJKRkBV4rFAMk5uXBuCxBEUqoRKVaFoSusN6buSqzoG5tgnxWHr4_PaW86Y-myNRa7xtKmpi_lpujY6tAaOrNN3zqK9ZrOO0cfmqyojfWxZ7RdWZuqKukRnDZ211d4Sc5yrJy5-t1j8jp9XE2e2GI5m0_uFywTMXQsznKUkUwVYpqqAJJ1kqokiEJ_TXkeYioUZipDiRwytY5BrEVogigVoDAP5JjcDL2tbd574zq9bXpb-5daxEqpGEIpPCUGKrONc9bkurXlDu1Bc9A_RvVgVHuj-mhU731IDiHnYW_M_lX_k_oGPkB8LA</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Shi, Yun</creator><creator>Ren, Guangzhen</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-4197-0367</orcidid></search><sort><creationdate>20230401</creationdate><title>The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula</title><author>Shi, Yun ; Ren, Guangzhen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-7cfa363b8aabb8409d9b89465a36b1f5ab28ac8ca3a10c8d702d25e46b208af43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Complex variables</topic><topic>Lie groups</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shi, Yun</creatorcontrib><creatorcontrib>Ren, Guangzhen</creatorcontrib><collection>CrossRef</collection><jtitle>Advances in applied Clifford algebras</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shi, Yun</au><au>Ren, Guangzhen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula</atitle><jtitle>Advances in applied Clifford algebras</jtitle><stitle>Adv. Appl. Clifford Algebras</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>33</volume><issue>2</issue><artnum>22</artnum><issn>0188-7009</issn><eissn>1661-4909</eissn><abstract>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
H
n
×
R
r
.
Then we establish the Bochner–Martinelli type formula for tangential
k
-Cauchy–Fueter operator on stratified right-type groups.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00006-023-01267-x</doi><orcidid>https://orcid.org/0000-0002-4197-0367</orcidid></addata></record> |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Complex variables Lie groups Mathematical and Computational Physics Mathematical Methods in Physics Physics Physics and Astronomy Theoretical |
| title | The Tangential k-Cauchy–Fueter Operator on Right-Type Groups and Its Bochner–Martinelli Type Formula |
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