Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.3893
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dc.contributor.authorKruse, Karsten-
dc.date.accessioned2021-11-15T12:32:07Z-
dc.date.available2021-11-15T12:32:07Z-
dc.date.issued2021-10-19-
dc.identifier.citationCollectanea Mathematica (in Press) : (2021)de_DE
dc.identifier.issn2038-4815de_DE
dc.identifier.urihttp://hdl.handle.net/11420/10923-
dc.description.abstractThis paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator ∂¯ on spaces EV(Ω, E) of C∞-smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights V. Vector-valued means that these functions have values in a locally convex Hausdorff space E over C. We derive a counterpart of the Grothendieck-Köthe-Silva duality O(C\ K) / O(C) ≅ A(K) with non-empty compact K⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of ∂¯ : EV(Ω, E) → EV(Ω, E) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on EV(Ω, C).en
dc.language.isoende_DE
dc.publisherSpringerde_DE
dc.relation.ispartofCollectanea mathematicade_DE
dc.rightsCC BY 4.0de_DE
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de_DE
dc.subjectCauchy-Riemannde_DE
dc.subjectParameter dependencede_DE
dc.subjectSmoothde_DE
dc.subjectSolvabilityde_DE
dc.subjectVector-valuedde_DE
dc.subjectWeightde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleThe inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holesde_DE
dc.typeArticlede_DE
dc.identifier.doi10.15480/882.3893-
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-882.0158624-
tuhh.oai.showtruede_DE
tuhh.abstract.englishThis paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator ∂¯ on spaces EV(Ω, E) of C∞-smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights V. Vector-valued means that these functions have values in a locally convex Hausdorff space E over C. We derive a counterpart of the Grothendieck-Köthe-Silva duality O(C\ K) / O(C) ≅ A(K) with non-empty compact K⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of ∂¯ : EV(Ω, E) → EV(Ω, E) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on EV(Ω, C).de_DE
tuhh.publisher.doi10.1007/s13348-021-00337-2-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.3893-
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
dc.relation.projectProjekt DEALde_DE
dc.rights.nationallicensefalsede_DE
dc.identifier.scopus2-s2.0-85117313444de_DE
local.status.inpresstruede_DE
local.type.versionacceptedVersionde_DE
local.publisher.peerreviewedtruede_DE
datacite.resourceTypeArticle-
datacite.resourceTypeGeneralJournalArticle-
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDKruse, Karsten-
item.openairetypeArticle-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidKruse, Karsten-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-1864-4915-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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