Vector-valued holomorphic and harmonic functions
Abstract: Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Vector-valued holomorphic and harmonic functions ; volume:3 ; number:1 ; year:2016 ; pages:68-76 ; extent:9
Concrete operators ; 3, Heft 1 (2016), 68-76 (gesamt 9)
- Creator
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Arendt, Wolfgang
- DOI
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10.1515/conop-2016-0007
- URN
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urn:nbn:de:101:1-2410301536157.829489897298
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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2025-08-15T07:32:02+0200
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Associated
- Arendt, Wolfgang
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