DC FieldValueLanguage
dc.contributor.authorKruse, Karsten-
dc.date.accessioned2021-11-15T06:25:34Z-
dc.date.available2021-11-15T06:25:34Z-
dc.date.issued2022-
dc.identifier.citationComplex Variables and Elliptic Equations 67: 2676 - 2707 (2022)de_DE
dc.identifier.issn1747-6941de_DE
dc.identifier.urihttp://hdl.handle.net/11420/10925-
dc.description.abstractWe derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator ∂ between spaces of weighted smooth Fréchet-valued functions. This is done by establishing an analog of Hörmander's theorem on the solvability of the inhomogeneous Cauchy-Riemann equation in a space of smooth ℂ-valued functions whose topologyis given by a whole family of weights. Our proof relies on a weakened variant of weak reducibility of the corresponding subspace of holomorphic functions in combination with the Mittag-Leffler procedure. Using tensor products, we deduce the corresponding result on the solvability of the inhomogeneous Cauchy-Riemann equation for Fréchet-valued functions.en
dc.language.isoende_DE
dc.publisherTaylor & Francisde_DE
dc.relation.ispartofComplex variables and elliptic equationsde_DE
dc.subject32W05de_DE
dc.subject35A01de_DE
dc.subject46A32de_DE
dc.subject46E40de_DE
dc.subjectCauchy–Riemannde_DE
dc.subjectFréchetde_DE
dc.subjectsmoothde_DE
dc.subjectsolvabilityde_DE
dc.subjectsurjectivede_DE
dc.subjectweightde_DE
dc.subjectMathematics - Functional Analysisde_DE
dc.subjectMathematics - Functional Analysisde_DE
dc.subject35A01, 32W05, 46A32, 46E40de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleSurjectivity of the ∂-operator between weighted spaces of smooth vector-valued functionsde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishWe derive sufficient conditions for the surjectivity of the Cauchy-Riemann operator ∂ between spaces of weighted smooth Fréchet-valued functions. This is done by establishing an analog of Hörmander's theorem on the solvability of the inhomogeneous Cauchy-Riemann equation in a space of smooth ℂ-valued functions whose topologyis given by a whole family of weights. Our proof relies on a weakened variant of weak reducibility of the corresponding subspace of holomorphic functions in combination with the Mittag-Leffler procedure. Using tensor products, we deduce the corresponding result on the solvability of the inhomogeneous Cauchy-Riemann equation for Fréchet-valued functions.de_DE
tuhh.publisher.doi10.1080/17476933.2021.1945587-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.startpage1de_DE
tuhh.container.endpage32de_DE
dc.identifier.arxiv1810.05069v2de_DE
dc.identifier.scopus2-s2.0-85109318405de_DE
tuhh.container.articlenumber1945587de_DE
local.status.inpressfalsede_DE
local.publisher.peerreviewedtruede_DE
datacite.resourceTypeArticle-
datacite.resourceTypeGeneralJournalArticle-
item.grantfulltextnone-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.creatorOrcidKruse, Karsten-
item.languageiso639-1en-
item.creatorGNDKruse, Karsten-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-1864-4915-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik (E)-
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