Harmonic Analysis and Applications

June 4-8, 2018


"Extended Gevrey regularity - new perspectives"

Tomic, Filip

We 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.

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