An example of a nuclear space in infinite dimensional holomorphy
Copyright policy )An example of a nuclear space in infinite dimensional holomorphy
LetU be an open subset of a complex locally convex spaceE, andH(U) the space of holomorphic functions fromU toC. If the dualE′ ofE is nuclear with respect to the topology generated by the absolutely convex compact subsets ofE, then it is shown thatH(U) endowed with the compact open topology is a nuclear space. In particular, ifE is the strong dual of a Frechet nuclear space, thenH(U) is a Frechet nuclear space.
- University College Dublin Ireland
General theory of locally convex spaces, Duality theory for topological vector spaces, Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), Topological linear spaces of continuous, differentiable or analytic functions
General theory of locally convex spaces, Duality theory for topological vector spaces, Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), Topological linear spaces of continuous, differentiable or analytic functions
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