Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights

Detalhes bibliográficos
Autor(a) principal: Anh, P. K.
Data de Publicação: 2017
Outros Autores: Castro, L. P., Thao, P. T., 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/10773/16734
Resumo: This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.
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spelling Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weightsFractional Fourier transformConvolutionHermite functionYoung's convolution inequalityIntegral equationThis paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.American Institute of Physics2018-07-20T14:00:59Z2017-01-27T00:00:00Z2017-01-272018-01-27T17:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16734eng1551-761610.1063/1.4972598Anh, P. K.Castro, L. P.Thao, P. T.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:RCAAP2024-02-22T11:31:59Zoai:ria.ua.pt:10773/16734Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:52:04.600567Repositório 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 Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
title Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
spellingShingle Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
Anh, P. K.
Fractional Fourier transform
Convolution
Hermite function
Young's convolution inequality
Integral equation
title_short Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
title_full Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
title_fullStr Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
title_full_unstemmed Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
title_sort Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
author Anh, P. K.
author_facet Anh, P. K.
Castro, L. P.
Thao, P. T.
Tuan, N. M.
author_role author
author2 Castro, L. P.
Thao, P. T.
Tuan, N. M.
author2_role author
author
author
dc.contributor.author.fl_str_mv Anh, P. K.
Castro, L. P.
Thao, P. T.
Tuan, N. M.
dc.subject.por.fl_str_mv Fractional Fourier transform
Convolution
Hermite function
Young's convolution inequality
Integral equation
topic Fractional Fourier transform
Convolution
Hermite function
Young's convolution inequality
Integral equation
description This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.
publishDate 2017
dc.date.none.fl_str_mv 2017-01-27T00:00:00Z
2017-01-27
2018-07-20T14:00:59Z
2018-01-27T17:00:00Z
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/10773/16734
url http://hdl.handle.net/10773/16734
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1551-7616
10.1063/1.4972598
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 American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
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
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