On integral operators generated by the Fourier transform and a reflection

Detalhes bibliográficos
Autor(a) principal: Castro, L. P.
Data de Publicação: 2015
Outros Autores: Guerra, R. C., Tuan, N. M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/14937
Resumo: We present a detailed study of structural properties for certain algebraic operators generated by the Fourier transform and a reflection. First, we focus on the determination of the characteristic polynomials of such algebraic operators, which, e.g., exhibit structural differences when compared with those of the Fourier transform. Then, this leads us to the conditions that allow one to identify the spectrum, eigenfunctions, and the invertibility of this class of operators. A Parseval type identity is also obtained, as well as the solvability of integral equations generated by those operators. Moreover, new convolutions are generated and introduced for the operators under consideration.
id RCAP_baa767ed85820d5c74d5e2b863e3a101
oai_identifier_str oai:ria.ua.pt:10773/14937
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling On integral operators generated by the Fourier transform and a reflectionCharacteristic polynomialsFourier transformReflectionAlgebraic integral operatorsInvertibilitySpectrumIntegral equationParseval identityConvolutionWe present a detailed study of structural properties for certain algebraic operators generated by the Fourier transform and a reflection. First, we focus on the determination of the characteristic polynomials of such algebraic operators, which, e.g., exhibit structural differences when compared with those of the Fourier transform. Then, this leads us to the conditions that allow one to identify the spectrum, eigenfunctions, and the invertibility of this class of operators. A Parseval type identity is also obtained, as well as the solvability of integral equations generated by those operators. Moreover, new convolutions are generated and introduced for the operators under consideration.Georgian National Academy of Sciences; A. Razmadze Mathematical Institute2015-12-09T12:54:29Z2015-12-07T00:00:00Z2015-12-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/14937eng1512-0015Castro, L. P.Guerra, R. C.Tuan, N. M.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:RCAAP2024-02-22T11:27:27Zoai:ria.ua.pt:10773/14937Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:24.531714Repositório 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 On integral operators generated by the Fourier transform and a reflection
title On integral operators generated by the Fourier transform and a reflection
spellingShingle On integral operators generated by the Fourier transform and a reflection
Castro, L. P.
Characteristic polynomials
Fourier transform
Reflection
Algebraic integral operators
Invertibility
Spectrum
Integral equation
Parseval identity
Convolution
title_short On integral operators generated by the Fourier transform and a reflection
title_full On integral operators generated by the Fourier transform and a reflection
title_fullStr On integral operators generated by the Fourier transform and a reflection
title_full_unstemmed On integral operators generated by the Fourier transform and a reflection
title_sort On integral operators generated by the Fourier transform and a reflection
author Castro, L. P.
author_facet Castro, L. P.
Guerra, R. C.
Tuan, N. M.
author_role author
author2 Guerra, R. C.
Tuan, N. M.
author2_role author
author
dc.contributor.author.fl_str_mv Castro, L. P.
Guerra, R. C.
Tuan, N. M.
dc.subject.por.fl_str_mv Characteristic polynomials
Fourier transform
Reflection
Algebraic integral operators
Invertibility
Spectrum
Integral equation
Parseval identity
Convolution
topic Characteristic polynomials
Fourier transform
Reflection
Algebraic integral operators
Invertibility
Spectrum
Integral equation
Parseval identity
Convolution
description We present a detailed study of structural properties for certain algebraic operators generated by the Fourier transform and a reflection. First, we focus on the determination of the characteristic polynomials of such algebraic operators, which, e.g., exhibit structural differences when compared with those of the Fourier transform. Then, this leads us to the conditions that allow one to identify the spectrum, eigenfunctions, and the invertibility of this class of operators. A Parseval type identity is also obtained, as well as the solvability of integral equations generated by those operators. Moreover, new convolutions are generated and introduced for the operators under consideration.
publishDate 2015
dc.date.none.fl_str_mv 2015-12-09T12:54:29Z
2015-12-07T00:00:00Z
2015-12-07
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/10773/14937
url http://hdl.handle.net/10773/14937
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1512-0015
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 Georgian National Academy of Sciences; A. Razmadze Mathematical Institute
publisher.none.fl_str_mv Georgian National Academy of Sciences; A. Razmadze Mathematical Institute
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
_version_ 1799137554479448064

Registros relacionados