We set $D$ to be a simply connected domain and we consider exhaustion function spaces,
$X_\infty(D)$ with the projective topology. We show that the
natural topology on the topological dual of $X_\infty(D)$, $(X_\infty(D))'$, is the inductive topology.
As a main application we assume that $D$ has a Jordan rectifiable boundary
$\partial D$, and $M\subset \partial D$ to be an open analytic arc
whose Lebesgue measure satisfies $0
@article{1195157132,
author = {Chailos, George},
title = {The topology of the class of functions representable by Carleman
type formulae, duality and applications},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {13},
number = {5},
year = {2007},
pages = { 629-639},
language = {en},
url = {http://dml.mathdoc.fr/item/1195157132}
}
Chailos, George. The topology of the class of functions representable by Carleman
type formulae, duality and applications. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp. 629-639. http://gdmltest.u-ga.fr/item/1195157132/