Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains

Sean Dineen

Annales de l'institut Fourier (1973)

  • Volume: 23, Issue: 3, page 155-185
  • ISSN: 0373-0956

Abstract

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In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for Π n = 1 ∞ C and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) N -projective limits of Frechet spaces with a basis;2) countable direct sums of Frechet spaces with a basis;3) nuclear spaces.

How to cite

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Dineen, Sean. "Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains." Annales de l'institut Fourier 23.3 (1973): 155-185. <http://eudml.org/doc/74136>.

@article{Dineen1973,
abstract = {In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for $\Pi ^\infty _\{n=1\}\{\bf C\}$ and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) $N$-projective limits of Frechet spaces with a basis;2) countable direct sums of Frechet spaces with a basis;3) nuclear spaces.},
author = {Dineen, Sean},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {155-185},
publisher = {Association des Annales de l'Institut Fourier},
title = {Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains},
url = {http://eudml.org/doc/74136},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Dineen, Sean
TI - Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 3
SP - 155
EP - 185
AB - In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for $\Pi ^\infty _{n=1}{\bf C}$ and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) $N$-projective limits of Frechet spaces with a basis;2) countable direct sums of Frechet spaces with a basis;3) nuclear spaces.
LA - eng
UR - http://eudml.org/doc/74136
ER -

References

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