Reference : How far is the Borel map from being surjective in quasianalytic ultradifferentiable c...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/221438
How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?,
English
Esser, Céline mailto [Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
Schindl, Gerhard [> >]
2018
Journal of Mathematical Analysis and Applications
Elsevier
Yes (verified by ORBi)
International
0022-247X
1096-0813
Atlanta
United States
[en] Spaces of ultradifferentiable functions ; Borel Map ; Quasianalyticity ; Genericity ; Prevalence ; Lineability ; Baire category
[en] The Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. In the literature, it is well known that the restriction of $j^{\infty}$ to the germs of quasianalytic ultradifferentiable classes which are strictly containing the real analytic functions can never be onto the corresponding sequence space. In this paper, we are interested in studying how large the image of $j^{\infty}$ is and we investigate the size and the structure of this image by using different approaches (Baire residuality, prevalence and lineability). We give an answer to this question in the very general setting of quasianalytic ultradifferentiable classes defined by weight matrices, which contains as particular cases the classes defined by a single weight sequence or by a weight function.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
http://hdl.handle.net/2268/221438
10.1016/j.jmaa.2018.06.037
https://doi.org/10.1016/j.jmaa.2018.06.037

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