On generalized definitions of ultradifferentiable classes

We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipović, N. Teofanov F. Tomić are special cases general framework spaces ultradifferentiable defined in terms weight matrices sense A. Rainer third author. study “beyond geometric growth factors” a sequence an exponent sequence, prove these new types admit matrix representation transfer known results from matrix-type to such non-standard setting.