Global Operator Calculus on Spin Groups

Detalhes bibliográficos
Autor(a) principal: Cerejeiras, P.
Data de Publicação: 2023
Outros Autores: Ferreira, M., Kähler, U., Wirth, J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.8/8660
Resumo: Acknowledgements The work of P. Cerejeiras, M. Ferreira, and U. Kähler was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT– “Fundação para a Ciência e a Tecnologia”, within project UIDB/04106/2020 and UIDP/04106/2020. The present paper was supported by the project “Global operator calculi on compact and non-compact Lie groups”, Ações Integradas Luso-Alemãs – Acção No. A-42/16. Funding Open access funding provided by FCT|FCCN (b-on).
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spelling Global Operator Calculus on Spin GroupsSpin groupSpin representationsDifference operatorsPseudo-differential operatorsFourier transformMicrolocal analysisElliptic operatorsGlobal hypoellipticityAcknowledgements The work of P. Cerejeiras, M. Ferreira, and U. Kähler was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT– “Fundação para a Ciência e a Tecnologia”, within project UIDB/04106/2020 and UIDP/04106/2020. The present paper was supported by the project “Global operator calculi on compact and non-compact Lie groups”, Ações Integradas Luso-Alemãs – Acção No. A-42/16. Funding Open access funding provided by FCT|FCCN (b-on).n 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.SpringerIC-OnlineCerejeiras, P.Ferreira, M.Kähler, U.Wirth, J.2023-07-04T15:45:26Z2023-05-172023-05-17T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/8660engCerejeiras, P., Ferreira, M., Kähler, U. et al. Global Operator Calculus on Spin Groups. J Fourier Anal Appl 29, 32 (2023). https://doi.org/10.1007/s00041-023-10015-51069-5869https://doi.org/10.1007/s00041-023-10015-51531-5851info: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:RCAAP2024-01-17T15:57:50Zoai:iconline.ipleiria.pt:10400.8/8660Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:51:20.075078Repositório 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.none.fl_str_mv IC-Online
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 Acknowledgements The work of P. Cerejeiras, M. Ferreira, and U. Kähler was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT– “Fundação para a Ciência e a Tecnologia”, within project UIDB/04106/2020 and UIDP/04106/2020. The present paper was supported by the project “Global operator calculi on compact and non-compact Lie groups”, Ações Integradas Luso-Alemãs – Acção No. A-42/16. Funding Open access funding provided by FCT|FCCN (b-on).
publishDate 2023
dc.date.none.fl_str_mv 2023-07-04T15:45:26Z
2023-05-17
2023-05-17T00:00:00Z
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/10400.8/8660
url http://hdl.handle.net/10400.8/8660
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Cerejeiras, P., Ferreira, M., Kähler, U. et al. Global Operator Calculus on Spin Groups. J Fourier Anal Appl 29, 32 (2023). https://doi.org/10.1007/s00041-023-10015-5
1069-5869
https://doi.org/10.1007/s00041-023-10015-5
1531-5851
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
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