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Topologies on the space of holomorphic functions

Complex Variables 2007-07-23 v2 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.0707.1876,
  title  = {Topologies on the space of holomorphic functions},
  author = {Steven G. Krantz},
  journal= {arXiv preprint arXiv:0707.1876},
  year   = {2007}
}

Comments

This is a revision of an earlier version of the paper