[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.
Disciplines :
Mathematics
Author, co-author :
Bastin, Françoise ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Esser, Céline ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
About Generic Properties of "Nowhere Analyticity"
Publication date :
08 May 2012
Event name :
Functional Analysis: Applications to Complex Analysis and Partial Differential Equations
Event organizer :
Paweł Domański (Adam Mickiewicz University Poznań), Michael Langenbruch (Carl von Ossietzky Universität Oldenburg)
Event place :
Poznan (Bedlewo), Poland
Event date :
du 6 mai au 12 mai 2012
Audience :
International
References of the abstract :
F. Bastin, C. Esser, S. Nicolay, A note about generic properties of "nowhere analyticity", preprint December 2011
