Abstract. Spaces of ultradifferentiable functions are subclasses of smooth functions with certain growth conditions on all their derivatives. In the literature two different approaches are considered, either using a weight sequence or using a weight function. We present a generalization, namely classes defined by weight matrices.
For such classes we characterize the quasianalyticity. We show that the Borel mapping restricted to the germs of any quasianalytic class in this framework strictly larger than the real analytic class is never onto the corresponding sequence space.
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