Publication
Global Operator Calculus on Spin Groups
| dc.contributor.author | Cerejeiras, P. | |
| dc.contributor.author | Ferreira, M. | |
| dc.contributor.author | Kähler, U. | |
| dc.contributor.author | Wirth, J. | |
| dc.date.accessioned | 2023-07-04T15:45:26Z | |
| dc.date.available | 2023-07-04T15:45:26Z | |
| dc.date.issued | 2023-05-17 | |
| dc.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). | pt_PT |
| dc.description.abstract | 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. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | 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 | pt_PT |
| dc.identifier.doi | https://doi.org/10.1007/s00041-023-10015-5 | pt_PT |
| dc.identifier.eissn | 1531-5851 | |
| dc.identifier.issn | 1069-5869 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/8660 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer | pt_PT |
| dc.relation | Center for Research and Development in Mathematics and Applications | |
| dc.relation | Center for Research and Development in Mathematics and Applications | |
| dc.relation.publisherversion | https://link.springer.com/article/10.1007/s00041-023-10015-5 | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | Spin group | pt_PT |
| dc.subject | Spin representations | pt_PT |
| dc.subject | Difference operators | pt_PT |
| dc.subject | Pseudo-differential operators | pt_PT |
| dc.subject | Fourier transform | pt_PT |
| dc.subject | Microlocal analysis | pt_PT |
| dc.subject | Elliptic operators | pt_PT |
| dc.subject | Global hypoellipticity | pt_PT |
| dc.title | Global Operator Calculus on Spin Groups | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Center for Research and Development in Mathematics and Applications | |
| oaire.awardTitle | Center for Research and Development in Mathematics and Applications | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT | |
| oaire.citation.issue | 32 | pt_PT |
| oaire.citation.title | Journal of Fourier Analysis and Applications | pt_PT |
| oaire.citation.volume | 29 | pt_PT |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| person.familyName | Ferreira | |
| person.givenName | Milton | |
| person.identifier.ciencia-id | CA19-2009-F26D | |
| person.identifier.orcid | 0000-0003-1816-8293 | |
| person.identifier.rid | A-2004-2015 | |
| person.identifier.scopus-author-id | 12144179800 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
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