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| arXiv:0707.1876 |
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Title: Topologies on the space of holomorphic functions
Authors: Steven G. Krantz
Categories: math.CV Complex Variables (math.AP Analysis of PDEs)
Comments: This is a revision of an earlier version of the paper
Report number: AIM 2007-35
MSC: 32A10
Abstract: We show that a fairly arbitrary Frechet space topology on the space of
holomorphic functions on a domain controls the topology of uniform convergence
on compact sets.In fact it turns out that the result we present can be proved more simply
using the closed graph theorem. However, we believe that the techniques
presented here may be used to prove a more interesting result. Details to
appear later.
Owner: Steven G. Krantz
Version 1: Thu, 12 Jul 2007 20:10:36 GMT
Version 2: Mon, 23 Jul 2007 20:31:18 GMT
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