Structural results for quaternionic Gabor frames

Detalhes bibliográficos
Autor(a) principal: Cerejeiras, Paula
Data de Publicação: 2018
Outros Autores: Hartmann, Stefan, Orelma, Heikki
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/24151
Resumo: We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well as modified versions of the Wexler–Raz biorthogonality and Ron–Shen duality based on the concept of correlation function. We end up with a characterization of tight quaternionic Gabor frames.
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spelling Structural results for quaternionic Gabor framesQuaternionic Gabor framesTwo-sided QWFTQuaternionic frame operatorJanssen’s representationWexler–Raz biorthogonalityFrame boundsWe study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well as modified versions of the Wexler–Raz biorthogonality and Ron–Shen duality based on the concept of correlation function. We end up with a characterization of tight quaternionic Gabor frames.Springer Verlag2019-11-01T00:00:00Z2018-11-01T00:00:00Z2018-11-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/24151eng0188-700910.1007/s00006-018-0901-8Cerejeiras, PaulaHartmann, StefanOrelma, Heikkiinfo: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:RCAAP2024-02-22T11:47:26Zoai:ria.ua.pt:10773/24151Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:57:54.546488Repositório 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 Structural results for quaternionic Gabor frames
title Structural results for quaternionic Gabor frames
spellingShingle Structural results for quaternionic Gabor frames
Cerejeiras, Paula
Quaternionic Gabor frames
Two-sided QWFT
Quaternionic frame operator
Janssen’s representation
Wexler–Raz biorthogonality
Frame bounds
title_short Structural results for quaternionic Gabor frames
title_full Structural results for quaternionic Gabor frames
title_fullStr Structural results for quaternionic Gabor frames
title_full_unstemmed Structural results for quaternionic Gabor frames
title_sort Structural results for quaternionic Gabor frames
author Cerejeiras, Paula
author_facet Cerejeiras, Paula
Hartmann, Stefan
Orelma, Heikki
author_role author
author2 Hartmann, Stefan
Orelma, Heikki
author2_role author
author
dc.contributor.author.fl_str_mv Cerejeiras, Paula
Hartmann, Stefan
Orelma, Heikki
dc.subject.por.fl_str_mv Quaternionic Gabor frames
Two-sided QWFT
Quaternionic frame operator
Janssen’s representation
Wexler–Raz biorthogonality
Frame bounds
topic Quaternionic Gabor frames
Two-sided QWFT
Quaternionic frame operator
Janssen’s representation
Wexler–Raz biorthogonality
Frame bounds
description We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well as modified versions of the Wexler–Raz biorthogonality and Ron–Shen duality based on the concept of correlation function. We end up with a characterization of tight quaternionic Gabor frames.
publishDate 2018
dc.date.none.fl_str_mv 2018-11-01T00:00:00Z
2018-11-01
2019-11-01T00:00:00Z
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/10773/24151
url http://hdl.handle.net/10773/24151
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0188-7009
10.1007/s00006-018-0901-8
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 Verlag
publisher.none.fl_str_mv Springer Verlag
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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