Global Operator Calculus on Spin Groups
In this paper, we use the representation theory of the group Spin ( m ) to develop aspects of the global symbolic calculus of pseudo-differential operators on Spin ( 3 ) and Spin ( 4 ) in the sense of Ruzhansky–Turunen–Wirth. A detailed study of Spin ( 3 ) and Spin ( 4 ) -representations is made inc...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2023-06, Vol.29 (3), Article 32 |
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| creator | Cerejeiras, P. Ferreira, M. Kähler, U. Wirth, J. |
| description | In this paper, we use the representation theory of the group
Spin
(
m
)
to develop aspects of the global symbolic calculus of pseudo-differential operators on
Spin
(
3
)
and
Spin
(
4
)
in the sense of Ruzhansky–Turunen–Wirth. A detailed study of
Spin
(
3
)
and
Spin
(
4
)
-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group
Spin
(
4
)
and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups. |
| doi_str_mv | 10.1007/s00041-023-10015-5 |
| format | Article |
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Spin
(
m
)
to develop aspects of the global symbolic calculus of pseudo-differential operators on
Spin
(
3
)
and
Spin
(
4
)
in the sense of Ruzhansky–Turunen–Wirth. A detailed study of
Spin
(
3
)
and
Spin
(
4
)
-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group
Spin
(
4
)
and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-023-10015-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Calculus ; Differential calculus ; Differential equations ; Finite differences ; Fourier Analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Partial Differential Equations ; Signal,Image and Speech Processing</subject><ispartof>The Journal of fourier analysis and applications, 2023-06, Vol.29 (3), Article 32</ispartof><rights>The Author(s) 2023</rights><rights>COPYRIGHT 2023 Springer</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c379t-cb57256e26246479b8d339442b888ef1269588411c3d01ca4174614184b1834a3</cites><orcidid>0000-0003-1816-8293 ; 0000-0001-7667-4595 ; 0000-0002-3950-4236 ; 0000-0002-9066-1819</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/s00041-023-10015-5$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-023-10015-5$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Cerejeiras, P.</creatorcontrib><creatorcontrib>Ferreira, M.</creatorcontrib><creatorcontrib>Kähler, U.</creatorcontrib><creatorcontrib>Wirth, J.</creatorcontrib><title>Global Operator Calculus on Spin Groups</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>In this paper, we use the representation theory of the group
Spin
(
m
)
to develop aspects of the global symbolic calculus of pseudo-differential operators on
Spin
(
3
)
and
Spin
(
4
)
in the sense of Ruzhansky–Turunen–Wirth. A detailed study of
Spin
(
3
)
and
Spin
(
4
)
-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group
Spin
(
4
)
and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Calculus</subject><subject>Differential calculus</subject><subject>Differential equations</subject><subject>Finite differences</subject><subject>Fourier Analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Partial Differential Equations</subject><subject>Signal,Image and Speech Processing</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kD1PwzAQhi0EEqXwB5giMTCl-PztsaqgIFXqAMyW4zhVqjQOdjLw7zEEiQ3dcB96n7vTi9At4BVgLB8SxphBiQktcw-85GdoAZxCyRWH81xjoXMt9CW6SumIMQEq6QLdb7tQ2a7YDz7aMcRiYzs3dVMqQl-8Dm1fbGOYhnSNLhrbJX_zm5fo_enxbfNc7vbbl816Vzoq9Vi6ikvChSeCMMGkrlRNqWaMVEop3wARmivFABytMTjLQDIBDBSrQFFm6RLdzXuHGD4mn0ZzDFPs80lDFDANWGGZVatZdbCdN23fhDFal6P2p9aF3jdtnq8l0xJAa50BMgMuhpSib8wQ25ONnwaw-XbQzA6a7KD5cdDwDNEZSlncH3z8--Uf6gtEim8H</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Cerejeiras, P.</creator><creator>Ferreira, M.</creator><creator>Kähler, U.</creator><creator>Wirth, J.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1816-8293</orcidid><orcidid>https://orcid.org/0000-0001-7667-4595</orcidid><orcidid>https://orcid.org/0000-0002-3950-4236</orcidid><orcidid>https://orcid.org/0000-0002-9066-1819</orcidid></search><sort><creationdate>20230601</creationdate><title>Global Operator Calculus on Spin Groups</title><author>Cerejeiras, P. ; Ferreira, M. ; Kähler, U. ; Wirth, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c379t-cb57256e26246479b8d339442b888ef1269588411c3d01ca4174614184b1834a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Calculus</topic><topic>Differential calculus</topic><topic>Differential equations</topic><topic>Finite differences</topic><topic>Fourier Analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Partial Differential Equations</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cerejeiras, P.</creatorcontrib><creatorcontrib>Ferreira, M.</creatorcontrib><creatorcontrib>Kähler, U.</creatorcontrib><creatorcontrib>Wirth, J.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cerejeiras, P.</au><au>Ferreira, M.</au><au>Kähler, U.</au><au>Wirth, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global Operator Calculus on Spin Groups</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>29</volume><issue>3</issue><artnum>32</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>In this paper, we use the representation theory of the group
Spin
(
m
)
to develop aspects of the global symbolic calculus of pseudo-differential operators on
Spin
(
3
)
and
Spin
(
4
)
in the sense of Ruzhansky–Turunen–Wirth. A detailed study of
Spin
(
3
)
and
Spin
(
4
)
-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group
Spin
(
4
)
and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-023-10015-5</doi><orcidid>https://orcid.org/0000-0003-1816-8293</orcidid><orcidid>https://orcid.org/0000-0001-7667-4595</orcidid><orcidid>https://orcid.org/0000-0002-3950-4236</orcidid><orcidid>https://orcid.org/0000-0002-9066-1819</orcidid><oa>free_for_read</oa></addata></record> |
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| issn | 1069-5869 1531-5851 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Abstract Harmonic Analysis Approximations and Expansions Calculus Differential calculus Differential equations Finite differences Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Operators (mathematics) Partial Differential Equations Signal,Image and Speech Processing |
| title | Global Operator Calculus on Spin Groups |
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