Abstract
Abstract
First, it will be shown that Banach spaces $$V$$ of harmonic or holomorphic functions with $$L^{p}$$ norm satisfy minimal norm property, i.e., in any set
$$V_{z,c}:=\{f\in V\>|\>f(z)=c\},$$
if nonempty, there is exactly one element with minimal norm. Later, it will be proved that this element depends continuously on a deformation of a norm and on an increasing sequence of domains in a precisely defined sense.
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