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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 28, 2016

Vector-valued holomorphic and harmonic functions

Wolfgang Arendt
From the journal Concrete Operators

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.

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Received: 2015-11-25
Accepted: 2016-3-8
Published Online: 2016-4-28

© 2016 Wolfgang Arendt

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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