On the extent of the (non) quasi-analytic classes
type: Item
instance of: scholarly article
title: On the extent of the (non) quasi-analytic classes
zbMATH Open document ID: 0701.46012
DOI: 10.1007/BF01246775
author: Jean Schmets
author: Manuel Valdivia
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 4148899
zbMATH Keywords: quasi-analytic class
zbMATH Keywords: Gevrey classes
MaRDI profile type: Publication
cites work: Differentiable, Nowhere Analytic Functions
cites work: Most Infinitely Differentiable Functions are Nowhere Analytic
cites work: Contribution à l'étude des fonctions dérivables d'une variable réelle
cites work: Sur quelques extensions de la notion de distribution
cites work: Q4009967
full work available at URL: https://doi.org/10.1007/bf01246775
OpenAlex ID: W2030461859
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description: scientific article; zbMATH DE number 4148899