115 research outputs found
Non-extendability of holomorphic functions with bounded or continuously extendable derivatives
We consider the spaces and
containing all holomorphic functions on an open set , such that all derivatives , , are bounded on , or continuously extendable
on , respectively. We endow these spaces with their natural
topologies and they become Fr\'echet spaces. We prove that the set of
non-extendable functions in each of these spaces is either void, or dense and
. We give examples where or not. Furthermore, we
examine cases where can be replaced by , or and the corresponding spaces
stay unchanged
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