Reference : How far is the Borel map from being surjective in quasianalytic ultradifferentiable c...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?,
Esser, Céline mailto [Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >]
Schindl, Gerhard [> >]
Journal of Mathematical Analysis and Applications
Yes (verified by ORBi)
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

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