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Concrete Operators

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Vector-valued holomorphic and harmonic functions

Wolfgang Arendt
Published Online: 2016-04-28 | DOI: https://doi.org/10.1515/conop-2016-0007


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.

Keywords: Holomorphic functions; Banach space; Harmonic functions; Dirichlet problem; Vitali’s Theorem


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About the article

Received: 2015-11-25

Accepted: 2016-03-08

Published Online: 2016-04-28

Citation Information: Concrete Operators, Volume 3, Issue 1, Pages 68–76, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2016-0007.

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© 2016 Wolfgang Arendt. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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