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Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis
Inspired by the classical Cauchy transform in L 2 ( ∂ B ( R ) ) , we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the L 2 -boundary values of Hermit...
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| Published in: | Complex analysis and operator theory 2024, Vol.18 (7) |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_issue | 7 |
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| container_title | Complex analysis and operator theory |
| container_volume | 18 |
| creator | He, Fuli Huang, Song |
| description | Inspired by the classical Cauchy transform in
L
2
(
∂
B
(
R
)
)
, we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the
L
2
-boundary values of Hermitian monogenic functions, we prove that every
f
∈
L
2
(
S
2
m
-
1
;
V
)
can be decomposed as a sum of boundary values of functions, which are
h
-monogenic inside and outside the unit ball respectively. |
| doi_str_mv | 10.1007/s11785-024-01609-y |
| format | article |
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L
2
(
∂
B
(
R
)
)
, we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the
L
2
-boundary values of Hermitian monogenic functions, we prove that every
f
∈
L
2
(
S
2
m
-
1
;
V
)
can be decomposed as a sum of boundary values of functions, which are
h
-monogenic inside and outside the unit ball respectively.</description><identifier>ISSN: 1661-8254</identifier><identifier>EISSN: 1661-8262</identifier><identifier>DOI: 10.1007/s11785-024-01609-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Mathematics ; Mathematics and Statistics ; Operator Theory</subject><ispartof>Complex analysis and operator theory, 2024, Vol.18 (7)</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. 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></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>He, Fuli</creatorcontrib><creatorcontrib>Huang, Song</creatorcontrib><title>Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis</title><title>Complex analysis and operator theory</title><addtitle>Complex Anal. Oper. Theory</addtitle><description>Inspired by the classical Cauchy transform in
L
2
(
∂
B
(
R
)
)
, we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the
L
2
-boundary values of Hermitian monogenic functions, we prove that every
f
∈
L
2
(
S
2
m
-
1
;
V
)
can be decomposed as a sum of boundary values of functions, which are
h
-monogenic inside and outside the unit ball respectively.</description><subject>Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operator Theory</subject><issn>1661-8254</issn><issn>1661-8262</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkE1LxDAURYMoOI7-AVcB19G8pPlajsM4IxTcqNuQTlPJUNOatGD_vdURvZt3F4fH5SB0DfQWKFV3GUBpQSgrCAVJDZlO0AKkBKKZZKd_XRTn6CLnA6WSKmMWaFu6Mfk44M1n72IOXcQu1rhk5L4bY-3ShF9dO_qMQ8Q7n97DEFzE6zY0TZdqvIqunXLIl-iscW32V793iV4eNs_rHSmfto_rVUl6EGog3kkPmksn915CXTVcFNxRo1xdCCcogwq4AlPVTs2QEBw4lWovvDZMGsaX6Ob4t0_dxzxrsIduTPOIbDnM0VxrOVP8SOU-hfjm0z8F1H4bs0djdjZmf4zZiX8Bu3ZdWg</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>He, Fuli</creator><creator>Huang, Song</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2024</creationdate><title>Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis</title><author>He, Fuli ; Huang, Song</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-ea6e1836a6ce61dbf3543a097ad45a5021b13719bda76a655313067c5e8926923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operator Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>He, Fuli</creatorcontrib><creatorcontrib>Huang, Song</creatorcontrib><jtitle>Complex analysis and operator theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>He, Fuli</au><au>Huang, Song</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis</atitle><jtitle>Complex analysis and operator theory</jtitle><stitle>Complex Anal. Oper. Theory</stitle><date>2024</date><risdate>2024</risdate><volume>18</volume><issue>7</issue><issn>1661-8254</issn><eissn>1661-8262</eissn><abstract>Inspired by the classical Cauchy transform in
L
2
(
∂
B
(
R
)
)
, we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the
L
2
-boundary values of Hermitian monogenic functions, we prove that every
f
∈
L
2
(
S
2
m
-
1
;
V
)
can be decomposed as a sum of boundary values of functions, which are
h
-monogenic inside and outside the unit ball respectively.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11785-024-01609-y</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1661-8254 |
| ispartof | Complex analysis and operator theory, 2024, Vol.18 (7) |
| issn | 1661-8254 1661-8262 |
| language | eng |
| recordid | cdi_proquest_journals_3111183886 |
| source | Springer Link |
| subjects | Analysis Mathematics Mathematics and Statistics Operator Theory |
| title | Laurent Expansion and L2-Boundary Values in Hermitian Clifford Analysis |
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