The structure of linear extension operators for \(C^m\)
Let \(C^m(E)\) denote the Banach space of restrictions to \(E,\) where \(E\subset R^n.\) It is known that \(T:C^m(E)\rightarrow C^m(\mathbb{R}^n)\) such that \(Tf=f\) on \(E\) for any \(f\in C^m(E).\) Here the author shows that \(T\) can be taken to have a simple form, but cannot be taken to have an even simpler form.
scientific article; zbMATH DE number 5177714
scientific article