Discrete Hardy spaces for bounded domains in Rn

Detalhes bibliográficos
Autor(a) principal: Cerejeiras, Paula
Data de Publicação: 2020
Outros Autores: Kähler, Uwe, Legatiuk, Anastasiia, Legatiuk, Dmitrii
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/29892
Resumo: Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in R^n. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.
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spelling Discrete Hardy spaces for bounded domains in RnDiscrete Dirac operatorDiscrete monogenic functionsDiscrete function theoryDiscrete Cauchy transformDiscrete boundary value problemsDiscrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in R^n. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.Springer; Birkhäuser2020-11-24T20:36:48Z2021-02-01T00:00:00Z2021-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/29892eng1661-825410.1007/s11785-020-01047-6Cerejeiras, PaulaKähler, UweLegatiuk, AnastasiiaLegatiuk, Dmitriiinfo: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:RCAAP2024-02-22T11:57:46Zoai:ria.ua.pt:10773/29892Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:02:05.421821Repositório 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 Discrete Hardy spaces for bounded domains in Rn
title Discrete Hardy spaces for bounded domains in Rn
spellingShingle Discrete Hardy spaces for bounded domains in Rn
Cerejeiras, Paula
Discrete Dirac operator
Discrete monogenic functions
Discrete function theory
Discrete Cauchy transform
Discrete boundary value problems
title_short Discrete Hardy spaces for bounded domains in Rn
title_full Discrete Hardy spaces for bounded domains in Rn
title_fullStr Discrete Hardy spaces for bounded domains in Rn
title_full_unstemmed Discrete Hardy spaces for bounded domains in Rn
title_sort Discrete Hardy spaces for bounded domains in Rn
author Cerejeiras, Paula
author_facet Cerejeiras, Paula
Kähler, Uwe
Legatiuk, Anastasiia
Legatiuk, Dmitrii
author_role author
author2 Kähler, Uwe
Legatiuk, Anastasiia
Legatiuk, Dmitrii
author2_role author
author
author
dc.contributor.author.fl_str_mv Cerejeiras, Paula
Kähler, Uwe
Legatiuk, Anastasiia
Legatiuk, Dmitrii
dc.subject.por.fl_str_mv Discrete Dirac operator
Discrete monogenic functions
Discrete function theory
Discrete Cauchy transform
Discrete boundary value problems
topic Discrete Dirac operator
Discrete monogenic functions
Discrete function theory
Discrete Cauchy transform
Discrete boundary value problems
description Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in R^n. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.
publishDate 2020
dc.date.none.fl_str_mv 2020-11-24T20:36:48Z
2021-02-01T00:00:00Z
2021-02
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/29892
url http://hdl.handle.net/10773/29892
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1661-8254
10.1007/s11785-020-01047-6
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; Birkhäuser
publisher.none.fl_str_mv Springer; Birkhäuser
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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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