The dual of the space of holomorphic functions on localy closed convex sets
Copyright policy )The dual of the space of holomorphic functions on localy closed convex sets
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN , endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q) 0 of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.
Inductive and projective limits in functional analysis, convolution operator, Laplace transform, multiplication operator, space of holomorphic germs, Spaces defined by inductive or projective limits (LB, LF, etc.), Topological linear spaces of continuous, differentiable or analytic functions, projective description, surjectivity
Inductive and projective limits in functional analysis, convolution operator, Laplace transform, multiplication operator, space of holomorphic germs, Spaces defined by inductive or projective limits (LB, LF, etc.), Topological linear spaces of continuous, differentiable or analytic functions, projective description, surjectivity
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