Discrete Hardy spaces for bounded domains in Rn

Bibliographic Details
Main Author: Cerejeiras, Paula
Publication Date: 2020
Other Authors: Kähler, Uwe, Legatiuk, Anastasiia, Legatiuk, Dmitrii
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/29892
Summary: 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.
id RCAP_8ffa31e10656af2435eda9dbe16f6016
oai_identifier_str oai:ria.ua.pt:10773/29892
network_acronym_str RCAP
network_name_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository_id_str https://opendoar.ac.uk/repository/7160
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:28:43Zoai:ria.ua.pt:10773/29892Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:09:58.262769Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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
format article
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833594350598094848

Similar Items