[en] A infinitely differentiable function f is is analytic at a point x if its Taylor series at this point converges to f on an open neighbourhood of x; if this is not the case, f has a singularity at x. A function with a singularity at each point of the interval is called nowhere analytic on the interval. In this talk, we show that the set of nowhere analytic functions is prevalent in the Frechet space C([0;1]). We get then a deeper result using Gevrey classes.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
[Université de Liège - ULg > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
