Vector-valued holomorphic and harmonic functions

• Autorzy: Wolfgang Arendt
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 68-76

Daty

otrzymano

2015-11-25

zaakceptowano

2016-03-08

online

2016-04-28

Twórcy

autor

Wolfgang Arendt

• Institute of Applied Analysis, University of Ulm, 89069 Ulm, Germany

Bibliografia

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• [4] W. Arendt, N. Nikolski: Vector-valued holomorphic functions revisited. Math. Z. 234 (2000), no. 4, 777–805.
• [5] W. Arendt, N. Nikolski: Addendum: Vector-valued holomorphic functions revisited. Math. Z. 252 (2006), 687–689.
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• [12] M. Yu. Kokwin: Sets of Uniqueness for Harmonic and Analytic Functions and diverse Problems for Wave equations. Math. Notes. 97 (2015), 376–383.
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Identyfikatory

DOI

10.1515/conop-2016-0007