On generalized definitions of ultradifferentiable classes (Q6110807)

An ultradifferentiable class is a class of functions that are more regular than \(C^\infty\). They come up in the investigation of differential or convolution operators. As the references of the present paper show, there is a long history of definitions of ultradifferentiable classes. One such generalization has been given by \textit{S.~Pilipović} et al. [Novi Sad J. Math. 45, No.~1, 125--142 (2015; Zbl 1460.46028)]. Their approach leads to ultradifferentiable classes that are larger than any Gevrey class. In the present paper it is shown that these classes of ultradifferentiable functions are a subset of the classes introduced in [\textit{A.~Rainer} and \textit{G.~Schindl}, Stud. Math. 224, No.~2, 97--131 (2014; Zbl 1318.26053)].