**"Extended Gevrey regularity - new perspectives"**
#### Tomic, FilipWe define and study classes of smooth functions which contains Gevrey functions. Derivatives of such functions are controlled by two-parameter dependent sequences which do not satisfy Komatsu's
condition (M.2)', known as "stability under differential operators". We present the result about superposition and inverse-closedness of such classes.
This lead us to our main result:
$$\WF_{0,\infty}(P(x,D)u)\subseteq \WF_{0,\infty}(u)\subseteq \WF_{0,\infty}(P(x,D)u) \cup {\rm Char}(P),$$
where $u$ is a Schwartz distribution, $P(x,D)$ is a partial differential operator with coefficients in our classes
and $\WF_{0,\infty}$ is the wave front set described in terms of new regularity conditions. |