Bases in spaces of ultradifferentiable functions with compact support
type: Item
instance of: scholarly article
title: Bases in spaces of ultradifferentiable functions with compact support
zbMATH Open document ID: 0627.46047
DOI: 10.1007/BF01449214
author: Michael Langenbruch
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164399
review text: Let \(I\subset {\mathbb{R}}\) be a compact interval and let \(D_{(M_ p)}(I)\) (and \(D_{\{M_ p\}}(I))\) be the spaces of ultradifferentiable functions with compact support in I of Beurling type (and of Roumieu type, resp.) in the sense of H. Komatsu. It is shown, that \(D_{(M_ p)}(I)\) (and \(D_{\{M_ p\}}(I)_ b')\) are linear topologically isomorphic to a power series space of infinite type (and of finite type, resp.), if \((M_ p)\) satisfies the conditions (M1), (M2) and (M3) of H. Komatsu. The proof is based on Pelczynski's trick: It is shown, that the function spaces and the corresponding sequence spaces contain each other as complemented subspaces. These projections are explicitely given, using certain optimal cut off functions. As an application it is shown, that the problems of E. Borel and H. Whitney may be solved by means of a linear and continuous operator for the ultradifferentiable functions of Beurling type, if \((M_ p)\) satisfies (M1), (M2) and (M3).
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 4019767
zbMATH Keywords: spaces of ultradifferentiable functions with compact support
zbMATH Keywords: Roumieu type
zbMATH Keywords: Pelczynski's trick
zbMATH Keywords: complemented subspaces
zbMATH Keywords: ultradifferentiable functions of Beurling type
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4019767