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dc.contributor.authorMoschonas, Dionysios
dc.contributor.authorNestoridis, Vassili
dc.date.accessioned2017-10-25T08:20:08Z
dc.date.available2017-10-25T08:20:08Z
dc.date.issued2017-10-21
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1318
dc.descriptionResearch in Pairs 2016en_US
dc.description.abstractWe consider the spaces $H_{F}^{\infty}(\Omega)$ and $\mathcal{A}_{F}(\Omega)$ containing all holomorphic functions $f$ on an open set $\Omega \subseteq \mathbb{C}$, such that all derivatives $f^{(l)}$, $l\in F \subseteq \mathbb{N}_0=\{ 0,1,...\}$, are bounded on $\Omega$, or continuously extendable on $\overline{\Omega}$, respectively. We endow these spaces with their natural topologies and they become Fr\'echet spaces. We prove that the set $S$ of non-extendable functions in each of these spaces is either void, or dense and $G_\delta$. We give examples where $S=\varnothing$ or not. Furthermore, we examine cases where $F$ can be replaced by $\widetilde{F}=\{ l\in \mathbb{N}_0:\min F \leqslant l \leqslant \sup F\}$, or $\widetilde{F}_0= \{l\in \mathbb{N}_0:0\leqslant l \leqslant \sup F\}$ and the corresponding spaces stay unchanged.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,30
dc.subjectDomain of Holomorphyen_US
dc.subjectBaire's Theoremen_US
dc.subjectGeneric Propertyen_US
dc.subjectBounded Holomorphic Functionsen_US
dc.subjectAnalytic Capacityen_US
dc.titleNon-Extendability of Holomorphic Functions with Bounded or Continuously Extendable Derivativesen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2017-30
local.scientificprogramResearch in Pairs 2016en_US
local.series.idOWP-2017-30
local.subject.msc30
dc.identifier.urnurn:nbn:de:101:1-201801093159
dc.identifier.ppn1658648463


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