## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Holomorphic functions on locally closed convex sets and projective descriptions

#### Abstract

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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 4 (2003), 491-503.

Dates
First available in Project Euclid: 5 December 2003

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1070645797

Digital Object Identifier
doi:10.36045/bbms/1070645797

Mathematical Reviews number (MathSciNet)
MR2040526

Zentralblatt MATH identifier
1086.46003

#### Citation

Bonet, José; Meise, Reinhold; Melikhov, Sergej N. Holomorphic functions on locally closed convex sets and projective descriptions. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 4, 491--503. doi:10.36045/bbms/1070645797. https://projecteuclid.org/euclid.bbms/1070645797