[en] We consider the space C_1(K) of real-valued continuously differentiable
functions on a compact set K included in R^d. We characterize the completeness
of this space and prove that the restriction space C_1(R^d|K) = {f|K : f in
C_1(R^d)} is always dense in C_1(K). The space C_1(K) is then compared with
other spaces of differentiable functions on compact sets.
Disciplines :
Mathematics
Author, co-author :
Loosveldt, Laurent ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
What are continuously differentiable functions on compact sets?
Alternative titles :
[fr] Quelles sont les fonctions continûment différentiables sur un ensemble compact?
Publication date :
31 August 2020
Event name :
International Conference on Generalized Functions
Event organizer :
Jasson Vindas Michael Ruzhansky Sandro Coriasco Andreas Debrouwere Iuliu Sorin Pop Hans Vernaeve
Event place :
Ghent, Belgium
Event date :
du 31 août 2020 au 4 septembre 2020
Audience :
International
References of the abstract :
https://cage.ugent.be/gf2020/booklet.pdf
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Commentary :
The results presented in this talk were obtained with Leonhard Frerick and Jochen Wengenroth (Universität Trier)
