Reference : How far is the Borel map from being surjective in quasianalytic ultradifferentiable c...
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/2268/221438
 Title : How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?, Language : English Author, co-author : Esser, Céline [Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes >] Schindl, Gerhard [> >] Publication date : 2018 Journal title : Journal of Mathematical Analysis and Applications Publisher : Elsevier Peer reviewed : Yes (verified by ORBi) Audience : International ISSN : 0022-247X e-ISSN : 1096-0813 City : Atlanta Country : United States Keywords : [en] 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. Funders : Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS Permalink : http://hdl.handle.net/2268/221438 DOI : 10.1016/j.jmaa.2018.06.037 Commentary : https://doi.org/10.1016/j.jmaa.2018.06.037

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