Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 10, Number 4 (2003), 491-503.
Holomorphic functions on locally closed convex sets and projective descriptions
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.
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 4 (2003), 491-503.
First available in Project Euclid: 5 December 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46E10: Topological linear spaces of continuous, differentiable or analytic functions
Secondary: 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
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