Extension of ultradifferentiable functions of Roumieu type
type: Item
instance of: scholarly article
title: Extension of ultradifferentiable functions of Roumieu type
zbMATH Open document ID: 0633.46026
DOI: 10.1007/BF01194025
author: Michael Langenbruch
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Let \(K\subset {\mathbb{R}}^ n\) be a compact convex set and let \(E_{\{M_ j\}}(K)\) denote the ultradifferentiable functions of Roumieu type on K. It is shown, that there is no continuous linear extension operator \(T: E_{\{M_ j\}}(K)\to E_{\{M_ j\}}(J)\), if the sequence \((M_ j)\) is regular (\(K\subset\overset\circ J\subset {\mathbb{R}}^ n)\). This especially holds for the Gevrey sequence \(M_ j=(j!)^ s\), \(s>1\). The proof uses the category of tame (F)-spaces and an appropriate variant of the property (DN), which was introduced by D. Vogt to characterize the subspaces of (nuclear) power series spaces of finite type.
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 4030233
zbMATH Keywords: ultradifferentiable functions of Roumieu type
zbMATH Keywords: continuous linear extension operator
zbMATH Keywords: Gevrey sequence
zbMATH Keywords: tame (F)-spaces
zbMATH Keywords: property (DN)
MaRDI profile type: Publication
cites work: Ultradifferentiable Functions on Compact Intervals
cites work: Bases in spaces of ultradifferentiable functions with compact support
cites work: Whitney's extension theorem for ultradifferentiable functions of Beurling type
cites work: Linear Extension Operators for Ultradifferentiable Functions of Beurling Type on Compact Sets
cites work: On E. Borel's theorem
cites work: Eine Charakterisierung der Potenzreihenraeume von endlichem Typ und ihre Folgerungen
full work available at URL: https://doi.org/10.1007/bf01194025
OpenAlex ID: W2068960662
description: scientific article; zbMATH DE number 4030233