Bulletin of the Belgian Mathematical Society - Simon Stevin

Holomorphic functions on locally closed convex sets and projective descriptions

José Bonet, Reinhold Meise, and Sergej N. Melikhov

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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.

Article information

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

First available in Project Euclid: 5 December 2003

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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]

Weighted spaces of entire functions weighted inductive limits projective description spaces of analytic functions locally closed convex set


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

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