Holomorphic functions on locally closed convex sets and projective descriptions
Bonet, José ; Meise, Reinhold ; Melikhov, Sergej N.
Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 491-503 / Harvested from Project Euclid
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Let $Q$ be a bounded, convex and locally closed subset of \ $\C^N$, let $H(Q)$ be the space of all functions which are holomorphic on an open neighborhood of $Q$. We endow $H(Q)$ with its projective topology. We show that the topology of the weighted inductive limit of Fr\'echet spaces of entire functions which is obtained as the Laplace transform of the strong dual to $H(Q)$ can be described be means of canonical weighted seminorms if and only if the intersection of $Q$ with each supporting hyperplane to the closure of $Q$ is compact. We also find conditions under which this (LF)-space of entire functions coincides algebraically with its projective hull.
Publié le : 2003-09-14
Classification:  Weighted spaces of entire functions,  weighted inductive limits,  projective description,  spaces of analytic functions,  locally closed convex set,  46E10,  46A13 
@article{1070645797,
     author = {Bonet, Jos\'e and Meise, Reinhold and Melikhov, Sergej N.},
     title = {Holomorphic functions on
locally closed convex sets and projective descriptions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 491-503},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1070645797}
}

Bonet, José; Meise, Reinhold; Melikhov, Sergej N. Holomorphic functions on
locally closed convex sets and projective descriptions. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  491-503. http://gdmltest.u-ga.fr/item/1070645797/