On integral operators generated by the Fourier transform and a reflection
Autor(a) principal: | |
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Data de Publicação: | 2015 |
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/10773/14937 |
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. |
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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 |
|
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1799137554479448064 |