Definition:Weakly Analytic Function
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Definition
Let $U$ be an open subset of $\C$.
Let $\struct {X, \norm {\, \cdot \,} }$ be a Banach space over $\C$.
Let $\struct {X^\ast, \norm {\, \cdot \,}_{X^\ast} }$ be the normed dual space of $\struct {X, \norm {\, \cdot \,} }$.
Let $f : U \to X$ be a mapping.
We say that $f$ is weakly analytic if and only if:
- for each $\phi \in X^\ast$, $\phi \circ f : U \to \C$ is analytic.
Also see
Sources
- 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $3.2$: Integration of continuous vector-valued functions