On the extent of the (non) quasi-analytic classes
We essentially prove: a) every non quasi-analytic class \(C^{\{M_ n\}}({\mathbb{R}})\) contains a vector subspace of dimension \(2^{\aleph_ 0}\), the nonzero elements of which are nowhere quasi-analytic, b) let \(C^{(M_ n)}({\mathbb{R}})\) be a non-quasi-analytic class and \(C^{(P_ n)}({\mathbb{R}})\) be a quasi-analytic class. The set \({\mathcal D}\) of the elements of \(C^{(M_ n)}({\mathbb{R}})\) which are somewhere in \(C^{\{P_ n\}}\) is a first category set in \(C^{(M_ n)}({\mathbb{R}}).\) Applications to the Gevrey classes are given.
scientific article; zbMATH DE number 4148899
scientific article