Inverse closedness and localization in extended Gevrey regularity

Abstract

© 2017, Springer International Publishing. We consider classes E τ,σ (U) of ultradifferentiable functions which are extension of Gevrey classes, and prove that such classes are inverse closed. This result is used to construct an element from E τ,σ (U) which is not a Gevrey regular function. Furthermore, we show that the singular support of a distribution u∈ D ′ (U) related to local regularity in E τ,σ (U) coincides with the standard projection of the corresponding wave front set WF τ,σ (u).