scholarly journals Reproducing Kernels and Composition Series for Spaces of Vector-Valued Holomorphic Functions on Tube Domains

1994 ◽  
Vol 124 (1) ◽  
pp. 181-204 ◽  
Author(s):  
B. Orsted ◽  
G. Zhang
Keyword(s):  
Holomorphic Functions ◽  
Reproducing Kernels ◽  
Composition Series ◽  
Tube Domains ◽  
Vector Valued

Vector-valued holomorphic functions revisited

2000 ◽  
Vol 234 (4) ◽  
pp. 777-805 ◽  
Author(s):  
W. Arendt ◽  
N. Nikolski
Keyword(s):  
Holomorphic Functions ◽  
Vector Valued

scholarly journals Vector-valued holomorphic and harmonic functions

2016 ◽  
Vol 3 (1) ◽  
pp. 68-76
Author(s):  
Wolfgang Arendt
Keyword(s):  
Banach Space ◽  
Convergence Theorem ◽  
Harmonic Functions ◽  
Dual Space ◽  
Holomorphic Functions ◽  
Bounded Functions ◽  
Vector Valued ◽  
Separating Subspace

AbstractHolomorphic 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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