Article (Scientific journals)
How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?,
Esser, Céline; Schindl, Gerhard
2018In Journal of Mathematical Analysis and Applications
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Keywords :
Spaces of ultradifferentiable functions; Borel Map; Quasianalyticity; Genericity; Prevalence; Lineability; Baire category
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Esser, Céline  ;  Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Schindl, Gerhard
Language :
English
Title :
How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?,
Publication date :
2018
Journal title :
Journal of Mathematical Analysis and Applications
ISSN :
0022-247X
eISSN :
1096-0813
Publisher :
Elsevier, Atlanta, United States
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Commentary :
https://doi.org/10.1016/j.jmaa.2018.06.037
Available on ORBi :
since 21 March 2018

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