Some applications of vector-valued analytic and harmonic functions

1986 ◽  
pp. 114-140 ◽  
Author(s):  
N. J. Kalton
Keyword(s):  
Harmonic 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.

scholarly journals Extension of vector-valued holomorphic and harmonic functions

2007 ◽  
Vol 183 (3) ◽  
pp. 225-248 ◽  
Author(s):  
José Bonet ◽  
Leonhard Frerick ◽  
Enrique Jordá
Keyword(s):  
Harmonic Functions ◽  
Vector Valued

Geometry of Spaces of Vector-Valued Harmonic Functions

1994 ◽  
Vol 46 (2) ◽  
pp. 274-283
Author(s):  
Patrick N. Dowling ◽  
Zhibao Hu ◽  
Mark A. Smith
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Unit Sphere ◽  
Harmonic Functions ◽  
Norm Convergence ◽  
Nikodym Property ◽  
Vector Valued

AbstractIt is shown that the space hp(D,X) has the Kadec-Klee property with respect to pointwise norm convergence in the Banach space X if and only if X has the Radon-Nikodym property and every point of the unit sphere of X is a denting point of the unit ball of X. In addition, it is shown that hp(D,X) is locally uniformly rotund if and only if X is locally uniformly rotund and has the Radon-Nikodym property.

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