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An example of a nuclear space in infinite dimensional holomorphy

Philip J. Boland Department of Mathematics, University College Dublin

TBD mathscidoc:1701.332455

Arkiv for Matematik, 15, (1), 87-91, 1975.10
Let$U$be an open subset of a complex locally convex space$E$, and$H(U)$the space of holomorphic functions from$U$to$C$. If the dual$E′$of$E$is nuclear with respect to the topology generated by the absolutely convex compact subsets of$E$, then it is shown that$H(U)$endowed with the compact open topology is a nuclear space. In particular, if$E$is the strong dual of a Fréchet nuclear space, then$H(U)$is a Fréchet nuclear space.
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@inproceedings{philip1975an,
  title={An example of a nuclear space in infinite dimensional holomorphy},
  author={Philip J. Boland},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203500284726264},
  booktitle={Arkiv for Matematik},
  volume={15},
  number={1},
  pages={87-91},
  year={1975},
}
Philip J. Boland. An example of a nuclear space in infinite dimensional holomorphy. 1975. Vol. 15. In Arkiv for Matematik. pp.87-91. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203500284726264.
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