Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces
| dc.creator | Glockner, Helge | |
| dc.date | 2007-01-06 | |
| dc.date | 2007-04-28 | |
| dc.date.accessioned | 2026-07-07T07:58:28Z | |
| dc.date.available | 2026-07-07T07:58:28Z | |
| dc.description | 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. | |
| dc.description | 15 pages (v2: references for linear independence of exponential polynomials added; proof replaced by easier argument) | |
| dc.identifier | https://arxiv.org/abs/math/0701197 | |
| dc.identifier | http://arxiv.org/abs/math/0701197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128017 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | 46G20 (primary) 26E05; 26E15; 26E20; 46T25 (secondary) | |
| dc.title | Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces | |
| dc.type | text |