Holomorphic extensions of weakly holomorphic functions in weighted spaces of holomorphic functions
Abstract
Let v be a weight on a domain D in a metrizable locally convex space E and F be a complete locally convex space. Denote H v ( D; F ) the weighted space of F -valued holomorphic functions on D; and A v ( D ) is a subspace of H v ( D; C ) with the closed unit ball is compact for the open compact topology. Using a linearization theorem of weighted spaces of holomorphic functions, in this paper we set up characterizations for M ⊂ D and W ⊂ F 0 such that every function f : M ! F can be holomorphically extended to the whole domain D in the case u ◦ f admits a holomorphic extension to D for every u 2 W