On certain extension theorems in the mixed Borel setting (Q1883345)

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.