Existence of basis in some Whitney function spaces
type: Item
instance of: scholarly article
title: Existence of basis in some Whitney function spaces
zbMATH Open document ID: 1098.46003
DOI: 10.1007/BF03322898
author: Mustafa Kesir
author: Mefharet Kocatepe
published in: Results in Mathematics
publication date: 2006-03-07T00:00:00Z
review text: In this article, it is shown that certain spaces of Whitney jets \(\mathcal{E}(K)\) defined on a Cantor type compact set \(K\) in the real line have a Schauder basis. The existence of continuous linear extension operators from \(\mathcal{E}(K)\) into \(C^{\infty}(\mathbb R)\) for compact sets \(K\) of this type was investigated by \textit{B.~Arslan, A.~P.\ Goncharov} and \textit{M.~Kocatepe} [Can.\ J.\ Math.\ 54, No.~2, 225--238 (2002; Zbl 1041.46016)]. The basis is not constructed explicitly; its existence is obtained using a result of \textit{A.~Aytuna, J.~Krone} and \textit{T.~Terzioglu} [Math.\ Ann.\ 283, No.~2, 193--202 (1989; Zbl 0643.46001)] on the existence of a basis in certain complemented subspaces of the space \(s\) of rapidly decreasing sequences. Alas, the numbers in the quotations to the references are missing in the text, which makes the reading of the paper a bit difficult.
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A35
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A63
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 5009756
zbMATH Keywords: Schauder basis
zbMATH Keywords: Fréchet spaces
zbMATH Keywords: spaces of Whitney jets
zbMATH Keywords: Cantor sets
reviewed by: José Bonet
MaRDI profile type: Publication
cites work: Spaces of Whitney Functions on Cantor-Type Sets
cites work: Complemented infinite type power series subspaces of nuclear Fréchet spaces
cites work: Q3847672
cites work: APPROXIMATE DIMENSION AND BASES IN NUCLEAR SPACES
cites work: Q4071669
cites work: Q3245480
cites work: Fortsetzungen von \(C^\infty\)-Funktionen, welche auf einer abgeschlossenen Menge in \(R^ n\) definiert sind
cites work: Charakterisierung der Unterräume von \((s)\)
description: scientific article; zbMATH DE number 5009756