Existence of basis in some Whitney function spaces
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.
scientific article; zbMATH DE number 5009756