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- W2951376488 abstract "For each positive integer k, we describe a map f from the complex plane to a suitable non-complete complex locally convex space such that f is k times continuously complex differentiable but not k+1 times, and hence not complex analytic. We also describe a complex analytic map from l^1 to a suitable complete complex locally convex space which is unbounded on each non-empty open subset of l^1. Furthermore, we present a smooth map from the real line to a non-complete locally convex space which is not real analytic although it is given locally by its Taylor series around each point. As a byproduct, we find that free locally convex spaces over subsets of the complex plane with non-empty interior are not Mackey complete." @default.
- W2951376488 created "2019-06-27" @default.
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- W2951376488 date "2007-01-06" @default.
- W2951376488 modified "2023-10-01" @default.
- W2951376488 title "Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces" @default.
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