Vector-valued holomorphic and harmonic functions

IF 0.3 Q4 MATHEMATICS
W. Arendt
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引用次数: 10

Abstract

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.
向量值全纯函数与调和函数
研究了Banach空间中带值的全纯函数和调和函数。根据与Nikolski[4]的联合文章给出的方法,证明了对于在Banach空间中有值的有界函数,在对偶空间的分离子空间中与泛函的复合是全纯的就足以推导出全纯。另一个结果是全纯函数的Vitali收敛定理。本文的主要新颖之处在于证明了巴拿赫空间中带值调和函数的类似结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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