  After defining classical weighted modulation spaces we show some basic
properties. In this work we additionally choose an approach in terms of the
frequency-uniform decomposition and a discussion on the weights of modulation
spaces leads to a definition of Gevrey-modulation spaces, where we leave the
Sobolev frame and proceed to the Gevrey frame in order to get better results.
We prove that Gevrey-modulation spaces are algebras under multiplication.
Moreover, we obtain a non-analytic superposition result which gives rise to
discuss the possibility to apply Gevrey-modulation spaces to non-linear partial
differential equations.

Analysis of PDEs