Generic results in classes of ultradifferentiable functions

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• 作者：C茅line Esser
• 关键词：Ultradifferentiable functions ; Denjoy&ndash ; Carleman classes ; Beurling spaces ; Roumieu spaces ; Residual sets ; Prevalent sets ; Shy sets ; Lineability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1 May, 2014
• 年：2014
• 卷：413
• 期：1
• 页码：378-391
• 全文大小：309 K

文摘

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 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.