On certain extension theorems in the mixed Borel setting
type: Item
instance of: scholarly article
title: On certain extension theorems in the mixed Borel setting
zbMATH Open document ID: 1073.46015
author: Jean Schmets
author: Manuel Valdivia
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-12T00:00:00Z
review text: The authors continue their detailed study of extension problems for infinitely differentiable functions and determine the range of the Borel mapping \(B\) on certain classes of ultradifferentiable functions, where \(B(f) := (f^{(\alpha)}(0))_{\alpha\in \mathbb{N}_0^n}\) for an infinitely differentiable function \(f\) defined on \( \mathbb{R}^n\). Using ideas of \textit{H.-J. Petzsche} [Math. Ann. 282, 299--313 (1988; Zbl 0633.46033)], the extensions are obtained by means of an explicit construction. For the Borel mapping, this extends previous extension results obtained for convex sets (instead of \(\{0\}\)) by \textit{J. Bonet, R. Meise} and \textit{B. A. Taylor} [North-Holland Math. Stud. 170, 97--111 (1992; Zbl 0769.46008)] and \textit{M. Langenbruch} [Manuscr. Math. 83, 123--143 (1994; Zbl 0836.46027)] using different methods.
reviewed by: Michael Langenbruch
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 26E10
zbMATH DE Number: 2107195
zbMATH Keywords: Borel theorem
zbMATH Keywords: ultradifferentiable functions
zbMATH Keywords: Beurling type
zbMATH Keywords: Roumieu type
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.10.006
OpenAlex ID: W2067595579
cites work: Q4015687
cites work: Surjectivity of the restriction map to a compact in classes of ultradifferentiable functions
cites work: Q3671563
cites work: Extension of ultradifferentiable functions
cites work: On E. Borel's theorem
cites work: Q3152416
DOI: 10.1016/J.JMAA.2003.10.006
description: scientific article; zbMATH DE number 2107195