Article (Scientific journals)
Generic results in classes of ultradifferentiable functions
Esser, Céline
2014In Journal of Mathematical Analysis and Applications, 413 (1), p. 378–391
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Keywords :
Ultradifferentiable functions; Denjoy–Carleman classes; Beurling spaces; Roumieu spaces; Residual sets; Prevalent sets; Shy sets; Lineability
Abstract :
[en] Let E be a Denjoy Carleman class of ultradifferentiable functions of Beurling type on the real line that strictly contains another class F of Roumieu type. We show that the set S of functions in E that are nowhere in the class F is large in the topological sense (it is residual), in the measure theoretic sense (it is prevalent), and that SU{0} contains an infinite dimensional linear subspace (it is lineable). Consequences for the Gevrey classes are given. Similar results are also obtained for classes of ultradifferentiable functions defined imposing conditions on the Fourier Laplace transform of the function.
Disciplines :
Mathematics
Author, co-author :
Esser, Céline  ;  Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Generic results in classes of ultradifferentiable functions
Publication date :
2014
Journal title :
Journal of Mathematical Analysis and Applications
ISSN :
0022-247X
eISSN :
1096-0813
Publisher :
Academic Press, San Diego, United States - California
Volume :
413
Issue :
1
Pages :
378–391
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
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since 18 December 2013

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