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Motivated by classical results for Gevrey spaces and their applications to nonlinear partial differential equations we define so-called Gevrey-modulation spaces. We establish analytic as well as non-analytic superposition results on Gevrey-modulation spaces. These results are extended to a special weighted modulation space where the weight increases stronger than any polynomial but less than as in the Gevrey case.

Non-analytic superposition results on modulation spaces with subexponential weights