Global operator calculus on spin groups
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/38324 |
Resumo: | 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. |
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7160 |
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Global operator calculus on spin groupsSpin groupSpin representationsDifference operatorsPseudo-differential operatorsFourier transformMicrolocal analysisElliptic operatorsGlobal hypoellipticityIn 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.Springer2023-07-03T14:03:35Z2023-01-01T00:00:00Z2023info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/38324eng1069-586910.1007/s00041-023-10015-5Cerejeiras, P.Ferreira, M.Kähler, U.Wirth, J.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:13:49Zoai:ria.ua.pt:10773/38324Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:08:22.411384Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Global operator calculus on spin groups |
title |
Global operator calculus on spin groups |
spellingShingle |
Global operator calculus on spin groups Cerejeiras, P. Spin group Spin representations Difference operators Pseudo-differential operators Fourier transform Microlocal analysis Elliptic operators Global hypoellipticity |
title_short |
Global operator calculus on spin groups |
title_full |
Global operator calculus on spin groups |
title_fullStr |
Global operator calculus on spin groups |
title_full_unstemmed |
Global operator calculus on spin groups |
title_sort |
Global operator calculus on spin groups |
author |
Cerejeiras, P. |
author_facet |
Cerejeiras, P. Ferreira, M. Kähler, U. Wirth, J. |
author_role |
author |
author2 |
Ferreira, M. Kähler, U. Wirth, J. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Cerejeiras, P. Ferreira, M. Kähler, U. Wirth, J. |
dc.subject.por.fl_str_mv |
Spin group Spin representations Difference operators Pseudo-differential operators Fourier transform Microlocal analysis Elliptic operators Global hypoellipticity |
topic |
Spin group Spin representations Difference operators Pseudo-differential operators Fourier transform Microlocal analysis Elliptic operators Global hypoellipticity |
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. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-03T14:03:35Z 2023-01-01T00:00:00Z 2023 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/38324 |
url |
http://hdl.handle.net/10773/38324 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1069-5869 10.1007/s00041-023-10015-5 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137736480784384 |