Convolutions and integral equations weighted by multi-dimensional Hermite functions

Detalhes bibliográficos
Autor(a) principal: Castro, L. P.
Data de Publicação: 2022
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/10773/33203
Resumo: We study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and use them as convolutions somehow associated with our integral equations. In the way, two Young-type inequalities are also obtained.
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spelling Convolutions and integral equations weighted by multi-dimensional Hermite functionsConvolutionYoung’s inequalityintegral equationHermite functionNormed ringWiener’s algebraWe study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and use them as convolutions somehow associated with our integral equations. In the way, two Young-type inequalities are also obtained.World Scientific Publishing2023-01-01T00:00:00Z2022-01-01T00:00:00Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/33203eng1793-557110.1142/S1793557122501510Castro, L. P.Guerra, R. C.Tuan, N. M.info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:03:39Zoai:ria.ua.pt:10773/33203Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:04:35.644329Repositório 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 Convolutions and integral equations weighted by multi-dimensional Hermite functions
title Convolutions and integral equations weighted by multi-dimensional Hermite functions
spellingShingle Convolutions and integral equations weighted by multi-dimensional Hermite functions
Castro, L. P.
Convolution
Young’s inequality
integral equation
Hermite function
Normed ring
Wiener’s algebra
title_short Convolutions and integral equations weighted by multi-dimensional Hermite functions
title_full Convolutions and integral equations weighted by multi-dimensional Hermite functions
title_fullStr Convolutions and integral equations weighted by multi-dimensional Hermite functions
title_full_unstemmed Convolutions and integral equations weighted by multi-dimensional Hermite functions
title_sort Convolutions and integral equations weighted by multi-dimensional Hermite functions
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 Convolution
Young’s inequality
integral equation
Hermite function
Normed ring
Wiener’s algebra
topic Convolution
Young’s inequality
integral equation
Hermite function
Normed ring
Wiener’s algebra
description We study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and use them as convolutions somehow associated with our integral equations. In the way, two Young-type inequalities are also obtained.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01T00:00:00Z
2022
2023-01-01T00:00:00Z
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/10773/33203
url http://hdl.handle.net/10773/33203
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1793-5571
10.1142/S1793557122501510
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv World Scientific Publishing
publisher.none.fl_str_mv World Scientific Publishing
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
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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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